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### 17. Difference Equations and Other Functional Equations

• 17.1. Difference Equations of Integer Argument
• 17.1.1. First-Order Linear Difference Equations of Integer Argument
• 17.1.2. First-Order Nonlinear Difference Equations of Integer Argument
• 17.1.3. Second-Order Linear Difference Equations with Constant Coefficients
• 17.1.4. Second-Order Linear Difference Equations with Variable Coefficients
• 17.1.5. Linear Difference Equations of Arbitrary Order with Constant Coefficients
• 17.1.6. Linear Difference Equations of Arbitrary Order with Variable Coefficients
• 17.1.7. Nonlinear Difference Equations of Arbitrary Order
• 17.2. Linear Difference Equations with a Single Continuous Variable
• 17.2.1. First-Order Linear Difference Equations
• 17.2.2. Second-Order Linear Difference Equations with Integer Differences
• 17.2.3. Linear mth-Order Difference Equations with Integer Differences
• 17.2.4. Linear mth-Order Difference Equations with Arbitrary Differences
• 17.3. Linear Functional Equations
• 17.3.1. Iterations of Functions and Their Properties
• 17.3.2. Linear Homogeneous Functional Equations
• 17.3.3. Linear Nonhomogeneous Functional Equations
• 17.3.4. Linear Functional Equations Reducible to Linear Difference Equations with Constant Coefficients
• 17.4. Nonlinear Difference and Functional Equations with a Single Variable
• 17.4.1. Nonlinear Difference Equations with a Single Variable
• 17.4.2. Reciprocal (Cyclic) Functional Equations
• 17.4.3. Nonlinear Functional Equations Reducible to Difference Equations
• 17.4.4. Power Series Solution of Nonlinear Functional Equations
• 17.5. Functional Equations with Several Variables
• 17.5.1. Method of Differentiation in a Parameter
• 17.5.2. Method of Differentiation in Independent Variables
• 17.5.3. Method of Substituting Particular Values of Independent Arguments
• 17.5.4. Method of Argument Elimination by Test Functions
• 17.5.5. Bilinear Functional Equations and Nonlinear Functional Equations Reducible to Bilinear Equations
• References for Chapter 17

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