A. D. Polyanin and A. V. Manzhirov Handbook of Integral Equations Second Edition, Updated, Revised and Extended Publisher: Chapman & Hall/CRC Press Publication Date: 14 February 2008 Number of Pages: 1144 Summary Preface Features Contents Index References

References

• Ablowitz, M. J. and Clarkson, P. A., Solitons, Non-linear Evolution Equations and Inverse Scattering, Cambridge Univ. Press, Cambridge, 1991.
• Abramowitz, M. and Stegun, I. A. (Editors), Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, National Bureau of Standards, Washington, 1964.
• Acrivos, A. and Shambre, P. L., Laminar boundary layer flows with surface reactions, Ind. Eng. Chem. Fundam., Vol. 49, pp. 1025–1029, 1957.
• Adams, R., Calculus: A Complete Course, 6th Edition, Pearson Education, Toronto, 2006.
• Aggarwala, B. D. and Nasim, C., Steady-state temperature in a quarter plane, Int. J. Math. & Math. Sci., Vol. 19, pp. 371–380, 1996.
• Akhiezer, N. I. and Glazman, I. M., Theory of Linear Operators in Hilbert Space [in Russian], Nauka, Moscow, 1966.
• Alexandrov, V. M., Asymptotic methods in the mechanics of continuous media: problems with mixed boundary conditions, Appl. Math. and Mech. (PMM), Vol. 57, No. 2, pp. 321–327, 1993.
• Alexandrov, V. M. and Kovalenko, E. V., Problems With Mixed Boundary Conditions in Continuum Mechanics [in Russian], Nauka, Moscow, 1986.
• Alexandrov, V. M., and Manzhirov, A. V., Two-dimensional integral equations in applied solid mechanics, Applied Mechanics and Technical Physics, No. 5, pp. 146–152, 1987.
• Alexandrov, V. M. and Mkhitaryan, S. M., Contact Problems for Bodies with Thin Coatings and Interlayers [in Russian], Nauka, Moscow, 1983.
• Andreev, A. V., Development of direct numerical integration methods f one-dimensional integro-differential equations in mechanics, Mech. Solids, Vol. 42, No. 2, pp. 209–222, 2007.
• Andreev, A. V., A method of determination of exponential type complex singularities in the solutions of singular integral equations with generalized kernels and conjugate variables, Mechanics of Solids, 2007 (to be published).
• Antimirov, M. Ya., Applied Integral Transforms, American Mathematical Society, Providence, Rhode Island, 1993.
• Anton, H., Bivens, I., and Davis, S., Calculus: Early Transcendental Single Variable, 8th Edition, John Wiley & Sons, New York, 2005.
• Agarwal, R. P., O'Regan, D., and Wong, P. J. Y., Positive Solutions of Differential, Difference and Integral Equations, Springer-Verlag, New York, 1998.
• Andreev, A. V., A method for numerical solution of complete singular integral equations with complex power-law singularities, Mech. Solids, Vol. 41, No. 1, pp. 76–87, 2006.
• Andreev, A. V., Direct numerical method for solving singular integral equations of the first kind with generalized kernels, Mech. Solids, Vol. 40, No. 1, pp. 104–119, 2005.
• Arutyunyan, N. Kh., A plane contact problem of creep theory, Appl. Math. and Mech. (PMM), Vol. 23, No. 5, pp. 901–924, 1959.
• Arutyunyan, N. Kh., Some Problems in the Theory of Creep, Pergamon Press, Oxford, 1966.
• Arutynyan, N. Kh., Manzhirov, A. V., and Naumov V. E., Contact Problems in Mechanics of Growing Solids [in Russian], Nauka, Moscow, 1991.
• Arutynyan, N. Kh., Manzhirov, A. V., Contact Problems in the Theory of Creep [in Russian], 1990, Izd-vo NAN RA, Erevan, 1999.
• Atkinson, K. E., Numerical Solution of Integral Equations of the Second Kind, Cambridge Univ. Press, Cambridge, 1997.
• Babenko, Yu. I., Heat and Mass Transfer: A Method for Computing Heat and Diffusion Flows [in Russian], Khimiya, Moscow, 1986.
• Bakhvalov, N. S., Numerical Methods [in Russian], Nauka, Moscow, 1973.
• Bateman, H., On the numerical solution of linear integral equations, Proc. Roy. Soc. (A), Vol. 100, No. 705, pp. 441–449, 1922.
• Bateman, H. and Erdelyi, A., Higher Transcendental Functions. Vol. 1, McGraw-Hill Book Co., New York, 1953.
• Bateman, H. and Erdelyi, A., Higher Transcendental Functions. Vol. 2, McGraw-Hill Book Co., New York, 1953.
• Bateman, H. and Erdelyi, A., Higher Transcendental Functions. Vol. 3, McGraw-Hill Book Co., New York, 1955.
• Bateman, H. and Erdelyi, A., Tables of Integral Transforms. Vol. 1, McGraw-Hill Book Co., New York, 1954.
• Bateman, H. and Erdelyi, A., Tables of Integral Transforms. Vol. 2, McGraw-Hill Book Co., New York, 1954.
• Beerends, R. J., ter Morschem, H. G., and van den Berg, J. C., Fourier and Laplace Transforms, Cambridge University Press, Cambridge, 2003.
• Bellman, R. and Cooke, K. L., Differential–Difference Equations, Academic Press, New York, 1963.
• Bellman, R. and Roth, R., The Laplace Transform, World Scientific Publishing Co., Singapore, 1984.
• Belotserkovskii, S. M. and Lifanov I. K., Method of Discrete Vortices, CRC Press, Boca Raton–New York, 1993.
• Beyer, W. H., CRC Standard Mathematical Tables and Formulae, CRC Press, Boca Raton, 1991.
• Bitsadze, A. V., Integral Equation of the First Kind, World Scientific, Singapore, 1995.
• Bracewell, R., The Fourier Transform and Its Applications, 3rd Edition, McGraw-Hill, New York, 1999.
• Bochner, S., Lectures on Fourier Integrals, Princeton Univ. Press, Princeton, 1959.
• Bochner, S. and Chandrasekharan, K. C., Fourier Transforms, Princeton Univ. Press, Princeton, 1949.
• Brakhage, H., Nickel, K., and Rieder, P., Auflosung der Abelschen Integralgleichung 2. Art, ZAMP, Vol. 16, Fasc. 2, S. 295–298, 1965.
• Bronshtein, I. N. and Semendyayev, K. A., Handbook of Mathematics, 4th Edition, Springer-Verlag, Berlin, 2004.
• Brunner, H., Collocation Methods for Volterra Integral and Related Functional Differential Equations, Cambridge University Press, Cambridge, 2004.
• Brychkov, Yu. A. and Prudnikov, A. P., Integral Transforms, In: Mathematical Encyclopedia, Vol. 2, pp. 589–590 [in Russian], Sovetskaya Entsiklopediya, Moscow, 1979.
• Brychkov, Yu. A. and Prudnikov, A. P., Integral Transforms of Generalized Functions, Gordon & Breach Sci. Publ., New York, 1989.
• Buchholz, H., The Confluent Hypergeometric Function, Springer-Verlag, New York, 1969.
• Bueckner, H. F., On a class of singular integral equations, J. Math. Anal. Appl., Vol. 14, pp. 392–426, 1966.
• Busbridge, I. W., Dual integral equations, Proc. Lond. Math. Soc., Vol. 44, pp. 115–129, 1938.
• Butkovskii, A. G., Characteristics of Systems With Distributed Parameters [in Russian], Nauka, Moscow, 1979.
• Cochran, J. A., The Analysis of Linear Integral Equations, McGraw-Hill Book Co., New York, 1972.
• Collatz, L., The Numerical Treatment of Differential Equations, Springer-Verlag, Berlin, 1960.
• Corduneanu, C., Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.
• Corduneanu, C., Integral Equations and Applications, Cambridge Univ. Press, Cambridge–New York, 1991.
• Courant, R. and Hilbert, D., Methods of Mathematical Physics. Vol. 1., Interscience Publ., New York, 1953.
• Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol. 2, Wiley-Interscience, New York, 1989.
• Courant, R. and John, F., Introduction to Calculus and Analysis, Vol. 1, Springer-Verlag, New York, 1999.
• Davenport, W. B. and Root, W. L., An Introduction to the Theory of Random Signals and Noise, McGraw-Hill Book Co., New York, 1958.
• David G. and Journe J.-L. A boundedness criterion for generalized Calderon–Zygmund operators, Ann. of Math., Vol. 120, pp. 371–397, 1984.
• Davis, B., Integral Transforms and Their Applications, Springer-Verlag, New York, 1978.
• Debnath, L. and Bhatta, B., Integral Transforms and Their Applications, 2nd Edition, Chapman & Hall/CRC Press, Boca Raton, 2007.
• Delves, L. M. and Mohamed J. L., Computational Methods for Integral Equations, Cambridge Univ. Press, Cambridge–New York, 1985.
• Demidovich, B. P., Maron, I. A., and Shuvalova E. Z., Numerical Methods. Approximation of Functions and Differential and Integral Equations [in Russian], Fizmatgiz, Moscow, 1963.
• Ditkin, V. A. and Prudnikov, A. P., Integral Transforms and Operational Calculus, Pergamon Press, New York, 1965.
• Doetsch, G., Handbuch der Laplace-Transformation. Theorie der Laplace-Transformation, Birkhauser Verlag, Basel–Stuttgart, 1950.
• Doetsch, G., Handbuch der Laplace-Transformation. Anwendungen der Laplace-Transformation, Birkhauser Verlag, Basel–Stuttgart, 1956.
• Doetsch, G., Einfuhrung in Theorie und Anwendung der Laplace-Transformation, Birkhauser Verlag, Basel–Stuttgart, 1958.
• Doetsch, G., Introduction to the Theory and Application of the Laplace Transformation, Springer-Verlag, Berlin, 1974.
• Duduchava, R., Singular Integral Equations with Fixed Singularities, Teubner, Leipzig, 1979.
• Dunford, N. and Schwartz J., Linear Operators. Part III. Spectral Operators, Interscience Publ., New York, 1971.
• Dwight, H. B., Tables of Integrals and Other Mathematical Data, Macmillan, New York, 1961.
• Dzhuraev, A., Methods of Singular Integral Equations, J. Wiley, New York, 1992.
• Edwards, C. H. and Penney, D., Calculus, 6th Edition, Pearson Education, Toronto, 2002.
• Edwards, R., Functional Analysis, Theory and Applications, Holt, Rinehart & Winston, New York, 1965.
• Erdogan, F. E., Complex Function Technique, In: Continuum Physics (Ed. A. C. Eringen), Vol. 2, pp. 523–603, Academic Press, New York, 1975.
• Erdogan, F. E., Gupta, G. D., and Cook, T. S., The Numerical Solutions of Singular Integral Equations, Mechanics of Fracture. Vol. 1. Methods of Analysis and Solutions of Crack Problems, pp. 368–425, Noordhoff Intern. Publ., Leyden, 1973.
• Estrada, R. and Kanwal, R. P., Singular Integral Equations, Birkhauser, Boston, 1999.
• Fenyo, S. and Stolle H. W., Theorie und Praxis der Linearen Integralgleichungen, Bd. 3, Birkhauser Verlag, Basel, 1984.
• Fock, V. A., Some integral equations of mathematical physics, Doklady AN SSSR, Vol. 26, No. 4–5, pp. 147–151, 1942.
• Frank-Kamenetskii, D. A., Diffusion and Heat Transfer in Chemical Kinetics [in Russian], Nauka, Moscow, 1987.
• Gakhov, F. D., Boundary Value Problems [in Russian], Nauka, Moscow, 1977.
• Gakhov, F. D., Boundary Value Problems, Dover Publ., New York, 1990.
• Gakhov, F. D. and Cherskii, Yu. I., Equations of Convolution Type [in Russian], Nauka, Moscow, 1978.
• Gantmakher, F. R., Non-symmetric Kellogg Kernels [in Russian], Doklady RAN, Vol. 1, No. 3, 1936.
• Gantmakher, F. R. and Krein, M. G., Oscillating matrices and small vibrations of mechanical systems [in Russian], Gostekhizdat, Moscow, 1950.
• Gohberg, I. C. and Krein, M. G., The Theory of Volterra Operators in a Hilbert Space and Its Applications [in Russian], Nauka, Moscow, 1967.
• Golberg, A. (Editor), Numerical Solution of Integral Equations, Plenum Press, New York, 1990.
• Gorenflo, R. and Vessella, S., Abel Integral Equations: Analysis and Applications, Springer-Verlag, Berlin–New York, 1991.
• Goursat, E., Cours d'Analyse Mathematique, III, Gauthier–Villars, Paris, 1923.
• Gradshteyn, I. S. and Ryzhik, I. M., Tables of Integrals, Series, and Products, 6th Edition, Academic Press, New York, 2000.
• Griffith, J. L., On the Hankel J-, Y and H transforms, Proc. Amer. Math. Soc., Vol. 9, No. 5, pp. 738–741, 1958.
• Gripenberg, G., Londen, S.-O., and Staffans, O., Volterra Integral and Functional Equations, Cambridge Univ. Press, Cambridge–New York, 1990.
• Guenther, R. B. and Lee, J. W., Partial Differential Equations of Mathematical Physics and Integral Equations, Dover Publications, New York, 1996.
• Gupalo, Yu. P., Polyanin, A. D., and Ryazantsev, Yu. S., Mass and Heat Transfer of Reacting Particles with the Flow [in Russian], Nauka, Moscow, 1985.
• Hackbusch, W., Integral Equations: Theory and Numerical Treatment, Birkhauser Verlag, Boston, 1995.
• Hansen, E. R., A Table of Series and Products, Printice Hall, Englewood Cliffs, London, 1975.
• Hirschman, I. I. and Widder, D. V., The Convolution Transform, Princeton Univ. Press, Princeton–New Jersey, 1955.
• Iovane, G., Lifanov, I.K., and Sumbatyan, M.A., On direct numerical treatment of hypersingular integral equations arising in mechanics and acoustics, arXiv:math-ph/0301034 v1 26 Jan 2003, pp. 1–19, 2003.
• Jentzch, R., Uber Integralgleichungen mit positivem Kern, J. Math., Vol. 141, p. 235, 1912.
• Jerry, A. J., Introduction to Integral Equations With Applications, Marcel Dekker, New York–Basel, 1985.
• Joseph, D. D., Stability of Fluid Motions, Springer-Verlag, Berlin, 1976.
• Kalandiya, A. I., Mathematical Methods of Two-Dimensional Elasticity, Mir Publ., Moscow, 1973.
• Kamke, E., Differentialgleichungen: Losungsmethoden und Losungen, Bd. 1, B. G. Teubner, Leipzig, 1977.
• Kantorovich, L. V. and Akilov, G. P., Functional Analysis in Normed Spaces, Macmillan, New York, 1964.
• Kantorovich, L. V. and Krylov, V. I., Approximate Methods of Higher Analysis, Interscience Publ., New York, 1958.
• Kanwal, R. P., Linear Integral Equations, Birkhauser Verlag, Boston, 1996.
• Karlin, S., Total positivity, Vol. 1, Stanford Univ. Press, Stanford, 1968.
• Karon, J. M., The sing-regularity properties of a class of Green's functions for ordinary differential equations, J. Diff. Equations, Vol. 6, p. 484, 1969.
• Kellogg, O. D., The oscilletion on functions of an orthogonal set, Amer. J. Math., Vol. 38, p. 1, 1916.
• Kellogg, O. D., Orthogonal functions sets arising from integral equations, Amer. J. Math., Vol. 40, p. 145, 1918.
• Kline, M., Calculus: An Intuitive and Physical Approach, 2nd Edition, Dover Publications, New York, 1998.
• Krein, M. G., Non-symmetric oscillating Green's functions of ordinary differential operators [in Russian], Doklady AN SSSR, Vol. 25, p. 643, 1939.
• Kolmogorov, A. N. and Fomin, S. V., Introductory Real Analysis, Prentice-Hall, Englewood Cliffs, 1970.
• Kolmogorov, A. N and Fomin, S. V., Elements of the Theory of Functions and Functional Analysis, Dover Publications, New York, 1999.
• Kondo, J., Integral Equations, Clarendon Press, Oxford, 1991.
• Korn, G. A. and Korn, T. M., Mathematical Handbook for Scientists and Engineers, 2nd Edition, Dover Publications, New York, 2000.
• Krantz, S. G., Handbook of Complex Variables, Birkhauser, Boston, 1999.
• Krasnoselskii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations, Macmillan, New York, 1964.
• Krasnov, M. L., Kiselev, A. I., and Makarenko, G. I., Problems and Exercises in Integral Equations, Mir Publ., Moscow, 1971.
• Krasnov, M. L., Integral Equations: Introduction to the Theory [in Russian], Nauka, Moscow, 1975.
• Krein, M. G. (Editor), Functional Analysis, 2nd Edition [in Russian], Nauka, Moscow, 1972.
• Krein, M. G., Integral equations on a half-line with kernels depending upon the difference of the arguments [in Russian], Uspekhi Mat. Nauk, Vol. 13, No. 5 (83), pp. 3–120, 1958.
• Kress, R., Linear Integral Equations, 2nd Edition, Springer-Verlag, New York, 1999.
• Kress, R., Numerical Analysis, Springer-Verlag, New York, 1998.
• Krylov, V. I., Bobkov, V. V., and Monastyrnyi, P. I., Introduction to the Theory of Numerical Methods. Integral Equations, Ill-Posed Problems, and Improvement of Convergence [in Russian], Nauka i Tekhnika, Minsk, 1984.
• Kythe, P. K. and Puri, P., Computational Methods for Linear Integral Equations, Birkhauser Verlag, Basel, 2002.
• Ladopoulos, E. G., Singular Integral Equations: Linear and Non-Linear Theory and Its Applications in Science and Engineering, Springer-Verlag, New York, 2000.
• Lavrentiev, M. M., Some Improperly Posed Problems of Mathematical Physics, Springer-Verlag, New York, 1967.
• Lavrentiev, M. M., Romanov, V. G., and Shishatskii, S. P., Ill-Posed Problems of Mathematical Physics and Analysis [in Russian], Nauka, Moscow, 1980.
• Lebedev, N. N., Special Functions and Their Applications, Prentice-Hall, Englewood Cliffs, 1965.
• LePage, W. R., Complex Variables and the Laplace Transform for Engineers, Dover Publications, New York, 1980.
• Levitan, B. M., Hilbert space, In: SpringerLink Encyclopaedia of Mathematics, 2001.
• Lifanov, I. K., Singular Integral Equations and Discrete Vortices, VSP, Amsterdam, 1996.
• Lifanov, I. K. Poltavskii, L. N., and Vainikko, G. M., Hypersingular and Singular Integral Equations and Their Applications, Chapman & Hall/CRC Press, Boca Raton, 2004.
• Linkov, A. M., Boundary Integral Equations in Elasticity Theory, Kluwer Academic Publ., Dordrecht, 2002.
• Linz, P., Analytical and Numerical Methods for Volterra Equations, SIAM, Philadelphia, 1987.
• Lovitt, W. V., Linear Integral Equations, Dover Publ., New York, 1950.
• Magnus, W., Oberhettinger, F., and Soni, R. P., Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd Edition, Springer-Verlag, Berlin, 1966.
• Mandal, B. N. and Mandal, N., Advances in Dual Integral Equations, Chapman & Hall/CRC Press, Boca Raton, 1999.
• Mangulis, V., Handbook of Series for Scientists and Engineers, Academic Press, New York, 1965.
• Manzhirov, A. V., A method of solution of two-dimensional integral equations of axisymmetric contact problems for solids with complex rheology, Applied Mathematics and Mechanics, Vol. 49, No. 6, pp. 1019–1025, 1985.
• Manzhirov, A. V., Contact problems for inhomogeneous aging viscoelastic solids, in I. I. Vorovich and V. M. Alexandrov (Editors), Mechanics of Contact Interactions [in Russian], pp. 549–565, Fizmatlit, Moscow, 2001.
• Manzhirov, A. V., Mixed integral equations of contact mechanics and tribology, in N. F. Morozov (Editor), Mixed Problems of Solid Mechanics. Materials of the Vth Russian Conference with International Participation [in Russian], pp. 222–226, Izd-vo Saratov. Un-ta, Saratov, 2005.
• Manzhirov, A. V. and Kazakov, K. E., Plane and axisymmetric contact problems for viscoelastic aging solids with surface-inhomogeneous coatings, in Problems in Solid and Rock Mechanics. Collection of Papers Devoted to the 75th Birthday of E. I. Shemyakin [in Russian], pp. 411–422, Fizmatlit, Moscow, 2006.
• McLachlan, N. W., Bessel Functions for Engineers, Clarendon Press, Oxford, 1955.
• McLean, W., Strongly Elliptic Systems and Boundary Integral Equations, Cambridge Univ. Press, Cambridge, 2000.
• Mikhailov, L. G., Integral Equations With Homogeneous Kernel of Degree -1 [in Russian], Donish, Dushanbe, 1966.
• Mikhlin, S. G. (Editor), Linear Equations of Mathematical Physics, Holt, Rinehart and Winston, New York, 1967.
• Mikhlin, S. G., Linear Integral Equations, Hindustan Publ. Corp., Delhi, 1960.
• Mikhlin, S. G. and Prossdorf, S., Singular Integral Operators, Springer-Verlag, Berlin–New York, 1986.
• Mikhlin, S. G. and Smolitskiy K. L., Approximate Methods for Solution of Differential and Integral Equations, American Elsevier Publ. Co., New York, 1967.
• Miles, J. W., Integral Transforms in Applied Mathematics, Cambridge Univ. Press, Cambridge, 1971.
• Moiseyev, N. G., and Popov G. Ya., The antiplane problem of a crack with edges touching planes where the constants of elasticity change, J. Appl. Math. and Mech. (PMM), Vol. 58, No. 4, pp. 713–725, 1994.
• Morse, P. M. and Feshbach, H., Methods of Theoretical Physics, Vol. 1, McGraw-Hill, New York, 1953.
• Muhly, P. S. and Xia, J., Calderon–Zygmund operators, local mean oscillation and certain automorphisms of the Toeplitz algebra, Amer. J. Math., Vol. 117, pp. 1157–1201, 1995.
• Muntz, H. M., Integral Equations [in Russian], GTTI, Leningrad, 1934.
• Murphy, G. M., Ordinary Differential Equations and Their Solutions, D. Van Nostrand, New York, 1960.
• Muskhelishvili N. I., Singular Integral Equations: Boundary Problems of Function Theory and Their Applications to Mathematical Physics, Dover Publ., New York, 1992.
• Naidenov, V. I. and Polyanin, A. D., Certain nonisothermal flows of fluid, J. Appl. Mech. & Tech. Physics, Vol. 31, No. 3, pp. 419-428, 1990.
• Nasim, C. and Aggarwala, B. D., On some dual integral equations, Indian J. Pure Appl. Math., Vol. 15, pp. 323–340, 1984.
• Naylor, D., On an integral transform, Int. J. Math. & Math. Sci., Vol. 9, No. 2, pp. 283–292, 1986.
• Nikiforov, A. F. and Uvarov, V. B., Special Functions of Mathematical Physics, Birkhauser Verlag, Basel, 1988.
• Nikolskii S. M., Quadrature Formulas [in Russian], Nauka, Moscow, 1979.
• Noble, B., Methods Based on Wiener–Hopf Technique for the Solution of Partial Differential Equations, Pergamon Press, London, 1958.
• Noble, B., The solution of Bessel function dual integral equations by a multiplying factor method, Proc. Camb. Phil. Soc., Vol. 59, pp. 351–362, 1963.
• Novikov, S. P., Manakov, S. V., Pitaevskii, L. B., and Zakharov, V. E., Theory of Solitons. The Inverse Scattering Method, Plenum Press, New York, 1984.
• Oberhettinger, F., Tables of Mellin Transforms, Springer-Verlag, New York, 1974.
• Oberhettinger, F., Tables of Bessel Transforms, Springer-Verlag, New York, 1972.
• Oberhettinger, F., Tables of Fourier Transforms and Fourier Transforms of Distributions, Springer-Verlag, Berlin, 1980.
• Oberhettinger, F. and Badii, L., Tables of Laplace Transforms, Springer-Verlag, New York, 1973.
• Oldham, K. B. and Spanier, J., The Fractional Calculus, Academic Press, London, 1974.
• Paley, E. A. C. and Wiener, N., Fourier Transforms in the Complex Domain, Amer. Math. Soc., New York, 1934.
• Petrov, A. G., Asymptotic expansions for thin axisymmetric cavities, J. Appl. Mech. Tech. Phys., Vol. 27, No. 5, pp. 667–672, 1986.
• Petrovsky, I. G., Lectures on Partial Differential Equations, Dover Publications, New York, 1991.
• Petrovskii, I. G., Lectures on the Theory of Integral Equations, Graylock Press, Rochester, 1957.
• Pinkus, A. and Zafrany, S., Fourier Series and Integral Transforms, Cambridge University Press, Cambridge, 1997.
• Pipkin, A. C., A Course on Integral Equations, Springer-Verlag, New York, 1991.
• Polyanin, A. D. and Manzhirov, A. V., Method of model solutions in the theory of linear integral equations [in Russian], Doklady AN, Vol. 354, No. 1, pp. 30–34, 1997.
• Polyanin, A. D. and Manzhirov, A. V., Handbook of Integral Equations, 1st Edition, CRC Press, Boca Raton, 1998.
• Polyanin, A. D. and Manzhirov, A. V., Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, Boca Raton, 2007.
• Polyanin, A. D. and Sergeev, Yu. A., Convective diffusion to a reacting particle in a fluid. Nonlinear surface reaction kinetics, Int. J. Heat Mass Transfer, Vol. 23, No. 9, pp. 1171–1182, 1980.
• Polyanin, A. D. and Zaitsev, V. F., Handbook of Exact Solutions for Ordinary Differential Equations, 2nd Edition, Chapman & Hall/CRC Press, Boca Raton, 2003.
• Polyanin, A. D. and Zaitsev, V. F., Handbook of Nonlinear Partial Differential Equations, Chapman & Hall/CRC Press, Boca Raton, 2004.
• Porter, D. and Stirling, D. S. G., Integral Equations: A Practical Treatment, from Spectral Theory to Applications, Cambridge Univ. Press, Cambridge–New York, 1990.
• Poularikas, A. D. (Editor), The Transforms and Applications Handbook, 2nd Edition, CRC Press, Boca Raton, 2000.
• Precup, R., Methods in Nonlinear Integral Equations, Springer-Verlag, New York, 2006.
• Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes in C. The Art of Scientific Computing, 2nd Edition, Cambridge Univ. Press, Cambridge, 1992.
• Privalov, I. I., Integral Equations [in Russian], ONTI, Moscow–Leningrad, 1935.
• Prossdorf, S. and Silbermann, B., Numerical Analysis for Integral and Related Operator Equations, Birkhauser Verlag, Basel–Boston, 1991.
• Prudnikov, A. P., Brychkov, Yu. A., and Marichev, O. I., Integrals and Series, Vol. 1, Elementary Functions, Gordon & Breach Sci. Publ., New York, 1986.
• Prudnikov, A. P., Brychkov, Yu. A., and Marichev, O. I., Integrals and Series, Vol. 2, Special Functions, Gordon & Breach Sci. Publ., New York, 1986.
• Prudnikov, A. P., Brychkov, Yu. A., and Marichev, O. I., Integrals and Series, Vol. 3, More Special Functions, Gordon & Breach Sci. Publ., New York, 1988.
• Prudnikov, A. P., Brychkov, Yu. A., and Marichev, O. I., Integrals and Series, Vol. 4, Direct Laplace Transforms, Gordon & Breach, New York, 1992.
• Prudnikov, A. P., Brychkov, Yu. A., and Marichev, O. I., Integrals and Series, Vol. 5, Inverse Laplace Transforms, Gordon & Breach, New York, 1992.
• Reed, M. and Simon, B., Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis, Academic Press, New York, 1972.
• Richtmyer, R., Principles of Advanced Mathematical Physics, Vol. 1, Springer-Verlag, Berlin, 1978.
• Riesz, F. and Sz.-Nagy, B., Functional Analysis, Ungar, New York, 1955.
• Rooney, P. G., A generalisation of an inversion formula for the Gauss transformation, Can. Math. Bull., Vol. 6, No. 1, 1963.
• Rudin, W., Functional Analysis, McGraw-Hill, New York, 1973.
• Sakhnovich, L. A., Integral Equations With Difference Kernels on Finite Intervals, Birkhauser Verlag, Basel–Boston, 1996.
• Samko, S. G., Hypersingular Integrals and Their Applications, Gordon & Breach Sci. Publ., New York, 2000.
• Samko, S. G., Kilbas, A. A., and Marichev, O. I., Fractional Integrals and Derivatives. Theory and Applications, Gordon & Breach Sci. Publ., New York, 1993.
• Sarason, D., Functions of vanishing mean oscillation, Trans. Amer. Math. Soc., Vol. 207, pp. 391–405, 1975.
• Savruk, M. P., Osiv, P. N., and Prokopchuk I. V., Numerical analysis in plane problems of crack theory, Naukova Dumka, Kiev, 1989.
• Savruk, M. P., Madenci, E., and Shkarayev S., Singular integral equations of the second kind with generalized Cauchy-type kernels and variable coefficients, Int. J. Numer. Meth. Eng., Vol. 45, pp. 1457–1470, 1999.
• Schmeidler, W., Integralgleichungen mit Anwendengen in Physik und Technik, Leipzig, 1950.
• Sherman, D. I., On a singular equation and its application to some problems of elasticity theory, Izv. AN ArmSSR, Vol. 22, No. 3, pp. 3–8, 1969.
• Slavyanov, S. Yu. and Lay, W., Special Functions: A Unified Theory Based on Singularities, Oxford University Press, Oxford, 2000.
• Smirnov, N. S., Introduction to the Theory of Nonlinear Integral Equations [in Russian], Gostekhizdat, Moscow, 1951.
• Smirnov, V. I., A Course in Higher Mathematics. Vol. 4. Part 1 [in Russian], Nauka, Moscow, 1974.
• Smirnov, V. I. and Lebedev, N. A., Functions of a Complex Variable: Constructive Theory [in Russian], Nauka, Moscow–Leningrad, 1964.
• Smithies, F., Integral Equations, Cambridge Univ. Press, Cambridge, 1958.
• Soni, K., Fractional integrals and Hankel transforms, Duke Math. J., Vol. 35, No. 2, pp. 313–319, 1968.
• Srivastava, H. M. and Buschman, R. G., Convolution Integral Equations with Special Function Kernels, Wiley Eastern, New Delhi, 1977.
• Sneddon, I., Fourier Transforms, Dover Publications, New York, 1995.
• Sneddon, I., The Use of Integral Transforms, McGraw-Hill, New York, 1972.
• Sullivan, M., Trigonometry, 7th Edition, Prentice Hall, Englewood Cliffs, 2004.
• Sutton, W. G. L., On the equation of diffusion in a turbulent medium, Proc. Poy. Soc., Ser. A, Vol. 138, No. 988, pp. 48–75, 1943.
• Sveshnikov, A. G. and Tikhonov, A. N., Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow, 1970.
• Szego, G., Orthogonal Polynomials, AMS, Providence, 1975.
• Theocaris, P. S. and Ioakimidis, N. I., Stress intensity factors at the tips of an antiplane shear crack terminating at a bimaterial interface, Int. J. of Fracture, Vol. 13, pp. 549–552, 1977.
• Theocaris, P. S., and Ioakimidis, N. I., A method of numerical solution of Cauchy-type singular integral equations with generalized kernels and arbitrary complex singularities, J. Comp. Phys., Vol. 30, No. 3, pp. 309–323, 1979.
• Tikhonov, A. N. and Arsenin, V. Ya., Methods for the Solution of Ill-Posed Problems [in Russian], Nauka, Moscow, 1979.
• Tikhonov, A. N. and Samarskii, A. A., Equations of Mathematical Physics, Dover Publications, New York, 1990.
• Titchmarsh, E. C., Hankel transforms, Proc. Cambridge Phol. Soc., Vol. 21, pp. 463–473, 1923.
• Titchmarsh, E. C., Theory of Fourier Integrals, Oxford Univ. Press, Oxford, 1937.
• Titchmarsh, E. C., Introduction to the Theory of Fourier Integrals, 3rd Edition, Chelsea Publishing, New York, 1986.
• Tricomi, F. G., Integral Equations, Dover Publ., New York, 1985.
• Tslaf, L. Ya., Variational Calculus and Integral Equations [in Russian], Nauka, Moscow, 1970.
• Tuan, Vu Kim, Some integral transforms of Fourier convolution type, Soviet Math. Dokl., Vol. 37, No. 3, pp. 669–673, 1988.
• Van der Pol, B. and Bremmer, H., Operational Calculus Based on the Two-Sides Laplace transform, Cambridge Univ. Press, Cambridge, 1955.
• Vasilieva, A. D. and Tikhonov, A. N., Integral Equations [in Russian], Izdat. Moskovskogo Universiteta, Moscow, 1989.
• Verlan', A. F. and Sizikov V. S., Integral Equations: Methods, Algorithms, and Programs [in Russian], Naukova Dumka, Kiev, 1986.
• Vinogradov, I. M. (Editor), Encyclopedia of Mathematics. Vol. 2 [in Russian], Sovetskaya Entsiklopediya, Moscow, 1979.
• Vladimirov, V. S., Equations of Mathematical Physics [in Russian], Nauka, Moscow, 1981.
• Volterra, V., Theory of Functionals and of Integral and Integro-Differential Equations, Dover Publ., New York, 1959.
• Vorovich, I. I., Aleksandrov, V. M., and Babeshko, V. A., Nonclassical Mixed Problems in the Theory of Elasticity [in Russian], Nauka, Moscow, 1974.
• Uflyand, Ya. S., Dual Integral Equations Method in Problems of Mathematical Physics [in Russian], Nauka, Leningrad, 1977.
• Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd Edition, Cambridge Univ. Press, Cambridge, 1952.
• Weisstein, E. W., CRC Concise Encyclopedia of Mathematics, 2nd Edition, CRC Press, Boca Raton, 2003.
• Whittaker, E. T. and Watson, G. N., A Course of Modern Analysis, Cambridge Univ. Press, Cambridge, 1958.
• Wiarda, G., Integralgleichungen unter besonderer Berucksichtigung der Anwendungen, Verlag und Druck von B. G. Teubner, Leipzig und Berlin, 1930.
• Wimp, J., Integral transforms involving Whittaker function, Glasnik Matematicki, Vol. 6, No. 1, pp. 67–70, 1971.
• Widder, D. V., An Introduction to Transform Theory, Acad. Press, New York, 1971.
• Widder, D. V., The Stieltjes transform, Trans. Amer. Math. Soc., Vol. 43, No. 1, pp. 7–60, 1939.
• Yosida, K., Functional Analysis, 6th Edition, Springer-Verlag, Berlin, 1980.
• Zabreyko, P. P., Koshelev, A. I., et al., Integral Equations: A Reference Text, Noordhoff Int. Publ., Leyden, 1975.
• Zakharov, V. E. and Shabat, A. B., A scheme for the integration of nonlinear evolutionary equations of mathematical physics by the inverse scattering method [in Russian], Funkts. Analiz i ego Prilozh., Vol. 8, No. 3, pp. 43–53, 1974.
• Zill, D. G. and Dewar, J. M., Trigonometry, 2nd Edition, McGraw-Hill, New York, 1990.
• Zwillinger, D., Handbook of Differential Equations, Academic Press, San Diego, 1989.
• Zwillinger, D., CRC Standard Mathematical Tables and Formulae, 31st Edition, CRC Press, Boca Raton, 2002.