Page 12 - Handbook Of Integral Equations

3.7. Equations Whose Kernels Contain Special Functions
3.7-1. Kernels Containing Bessel Functions
3.7-2. Kernels Containing Modified Bessel Functions
3.7-3. Other Kernels
3.8. Equations Whose Kernels Contain Arbitrary Functions
3.8-1. Equations With Degenerate Kernel
3.8-2. Equations Containing Modulus
3.8-3. Equations With Difference Kernel: K(x, t)= K(x – t)
b

3.8-4. Other Equations of the Form K(x, t)y(t) dt = F(x)
a
b

3.8-5. Equations of the Form K(x, t)y(·· ·) dt = F(x)
a
4. Linear Equations of the Second Kind With Constant Limits of Integration
4.1. Equations Whose Kernels Contain Power-Law Functions
4.1-1. Kernels Linear in the Arguments x and t
4.1-2. Kernels Quadratic in the Arguments x and t
4.1-3. Kernels Cubic in the Arguments x and t
4.1-4. Kernels Containing Higher-Order Polynomials in x and t
4.1-5. Kernels Containing Rational Functions
4.1-6. Kernels Containing Arbitrary Powers
4.1-7. Singular Equations
4.2. Equations Whose Kernels Contain Exponential Functions
4.2-1. Kernels Containing Exponential Functions
4.2-2. Kernels Containing Power-Law and Exponential Functions
4.3. Equations Whose Kernels Contain Hyperbolic Functions
4.3-1. Kernels Containing Hyperbolic Cosine
4.3-2. Kernels Containing Hyperbolic Sine
4.3-3. Kernels Containing Hyperbolic Tangent
4.3-4. Kernels Containing Hyperbolic Cotangent
4.3-5. Kernels Containing Combination of Hyperbolic Functions
4.4. Equations Whose Kernels Contain Logarithmic Functions
4.4-1. Kernels Containing Logarithmic Functions
4.4-2. Kernels Containing Power-Law and Logarithmic Functions
4.5. Equations Whose Kernels Contain Trigonometric Functions
4.5-1. Kernels Containing Cosine
4.5-2. Kernels Containing Sine
4.5-3. Kernels Containing Tangent
4.5-4. Kernels Containing Cotangent
4.5-5. Kernels Containing Combinations of Trigonometric Functions
4.5-6. A Singular Equation
4.6. Equations Whose Kernels Contain Inverse Trigonometric Functions
4.6-1. Kernels Containing Arccosine
4.6-2. Kernels Containing Arcsine
4.6-3. Kernels Containing Arctangent
4.6-4. Kernels Containing Arccotangent
4.7. Equations Whose Kernels Contain Combinations of Elementary Functions
4.7-1. Kernels Containing Exponential and Hyperbolic Functions
4.7-2. Kernels Containing Exponential and Logarithmic Functions
4.7-3. Kernels Containing Exponential and Trigonometric Functions
4.7-4. Kernels Containing Hyperbolic and Logarithmic Functions

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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