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The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:5. Integral Equations
Subcategory:5.3. Linear Equations of the First Kind with Constant Limits of Integration
Equation(s):$\displaystyle g(s)=s\int_{0}^{\infty}dtK(st)f(t)$,\hfill\break
where the Kernel  has a Mellin transform integral 

$\displaystyle \int_{0}^{\infty}dtK(t)t^{s-1}=F(s)$.\hfill\break
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle f(t)=\sum_{n=-\infty}^{\infty}\frac{a_{n}}{M(n+1+\alpha)}t^{n+\alpha}{$,\hfill\break
where $\dispalystyle  g(s)= \sum_{n=-\infty}^{\infty}a_{n}s^{-n} $,\hfill\break

and $\displaystyle F(n)=\int_{0}^{\infty}dtK(t)t^{n-1}$,\hfill\break

here $\displaystyle \alpha $,\hfill\break is a real number , this is because we can write our integral as

$\displaystyle g(s)=s\int_{0}^{\infty}dtK(st)f(t)=s\int_{0}^{\infty}dtK(st)(st)^{\alpha}u(t)=s^{\alpha}g(s)$,\hfill\break
Novelty:New equation(s) & solution(s) & transformation(s)
References:Borel Resummation and the Solution of Integral Equations e-print: http://vixra.org/abs/1304.0013
published at the 'Prespace time journal' http://www.prespacetime.com/index.php/pst/article/view/504
Author/Contributor's Details
Last name:Garcia
First name:Jose
Middle(s) name:Javier
Country:Spain
City:Portugalete
Affiliation:Graduate student at the UPV/EHU university
Statistic information
Submission date:Fri 16 Aug 2013 16:22
Edits by author:0

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