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Linear Equations of the First Kind with Variable Limit of Integration
- Equations Whose Kernels Contain Power-Law Functions
- Kernels Linear in the Arguments x and t.
- Kernels Quadratic in the Arguments x and t.
- Kernels Cubic in the Arguments x and t.
- Kernels Containing Higher-Order Polynomials in x and t.
- Kernels Containing Rational Functions.
- Kernels Containing Square Roots.
- Kernels Containing Arbitrary Powers.
- Two-Dimensional Equation of the Abel Type.
- Equations Whose Kernels Contain Exponential Functions
- Equations Whose Kernels Contain Hyperbolic Functions
- Kernels Containing Hyperbolic Cosine.
- Kernels Containing Hyperbolic Sine.
- Kernels Containing Hyperbolic Tangent.
- Kernels Containing Hyperbolic Cotangent.
- Kernels Containing Combinations of Hyperbolic Functions.
- Equations Whose Kernels Contain Logarithmic Functions
- Equations Whose Kernels Contain Trigonometric Functions
- Kernels Containing Cosine.
- Kernels Containing Sine.
- Kernels Containing Tangent.
- Kernels Containing Cotangent.
- Kernels Containing Combinations of Trigonometric Functions.
- Equations Whose Kernels Contain Inverse Trigonometric Functions
- Kernels Containing Arccosine.
- Kernels Containing Arcsine.
- Kernels Containing Arctangent.
- Kernels Containing Arccotangent.
- Equations Whose Kernels Contain Combinations of Elementary Functions
- Kernels Containing Exponential and Hyperbolic Functions.
- Kernels Containing Exponential and Logarithmic Functions.
- Kernels Containing Exponential and Trigonometric Functions.
- Kernels Containing Hyperbolic and Logarithmic Functions.
- Kernels Containing Hyperbolic and Trigonometric Functions.
- Kernels Containing Logarithmic and Trigonometric Functions.
- Equations Whose Kernels Contain Special Functions*
- Kernels Containing Error Function or Exponential Integral.
- Kernels Containing Sine and Cosine Integrals.
- Kernels Containing Fresnel Integrals.
- Kernels Containing Incomplete Gamma Functions.
- Kernels Containing Bessel Functions.
- Kernels Containing Modified Bessel Functions.
- Kernels Containing Legendre Polynomials.
- Kernels Containing Associated Legendre Functions.
- Kernels Containing Confluent Hypergeometric Functions.
- Kernels Containing Hermite Polynomials.
- Kernels Containing Chebyshev Polynomials.
- Kernels Containing Laguerre Polynomials.
- Kernels Containing Jacobi Theta Functions.
- Kernels Containing Other Special Functions.
- Equations Whose Kernels Contain Arbitrary Functions
- Equations with Degenerate Kernel: K(x,t) = g 1(x)h 1(t) + g 2(x)h 2(t).
- Equations with Difference Kernel: K(x,t) = K(x −t).
- Other Equations.
- Some Formulas and Transformations
Abstract
► Notation: f = f (x), g = g(x), h = h(x), K = K (x), and M = M (x) are arbitrary functions (these may be composite functions of the argument depending on two variables x and t); A, B, C, D, E, a, b, c, α, β, γ, λ, and μ are free parameters; and m and n are nonnegative integers.
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