## Advances in Dual Integral EquationsThe effectiveness of dual integral equations for handling mixed boundary value problems has established them as an important tool for applied mathematicians. Their many applications in mathematical physics have prompted extensive research over the last 25 years, and many researchers have made significant contributions to the methodology of solving and to the applications of dual integral equations. However, until now, much of this work has been available only in the form of research papers scattered throughout different journals. In Advances in Dual Integral Equations, the authors systematically present some of the recent developments in dual integral equations involving various special functions as kernel. They examine dual integral equations with Bessel, Legendre, and trigonometric functions as kernel plus dual integral equations involving inverse Mellin transforms. These can be particularly useful in studying certain mixed boundary value problems involving homogeneous media in continuum mechanics. However, when dealing with problems involving non-homogenous media, the corresponding equations may have different kernels. This application prompts the authors to conclude with a discussion of hybrid dual integral equations-mixed kernels with generalized associated Legendre functions and mixed kernels involving Bessel functions. Researchers in the theory of elasticity, fluid dynamics, and mathematical physics will find Advances in Dual Integral Equations a concise, one-stop resource for recent work addressing special functions as kernel. |

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### Contents

Dual integral equations with Bessel function kernel | 17 |

Dual integral equations with spherical harmonic kernel | 91 |

Dual integral equations with trigonometric function kernel | 134 |

Dual integral equations involving inverse Mellin transforms | 172 |

Hybrid dual integral equations | 187 |

Appendix | 199 |

216 | |

224 | |

### Common terms and phrases

7Г Л Abel integral equation Abel's inversion theorem arbitrary constant associated Legendre functions assume Babloian Bessel function boundary conditions boundary value problems class of dual consider the dual consider the pair cosech cosh cosh2 cosha coshí coshx cosTT/x defined determined dual integral equations Erdélyi explicit solution Fock inversion theorem Fourier cosine inversion Fredholm integral equation functions as kernel Hankel inversion theorem hybrid dual integral infinite integral equations arise integral equations involving integral representation integral transform integrating with respect interchanging the order inversion formula Jacobi polynomials Jc-ioo Jv(xt linear algebraic Mandal and Mandal Mehler Mellin transform method mixed boundary value multiplying Nasim obtain the solution order of integration P_i+iT(coshx pair of integral reduced satisfies second kind sinhx dx sinxt dt Sneddon t f(t tanhTTT trigonometric functions unknown constants unknown function Virchenko 1989 weight function гт тг

### References to this book

Generalized Associated Legendre Functions and Their Applications Nina Opanasivna Virchenko,Iryna Fedotova No preview available - 2001 |