Evaluation of integrals and the Mellin transform

DOI10.1007/BF01373648zbMath0725.44001OpenAlexW2057557595MaRDI QIDQ2276716

O. I. Marichev, Yu. A. Brychkov, A. P. Prudnikov

Publication date: 1991

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01373648

zbMATH Keywords

Mellin transformbibliographyhypergeometric functionsspecial functions

Mathematics Subject Classification ID

Other hypergeometric functions and integrals in several variables (33C70) Laplace transform (44A10) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions (33-00) General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral transforms (44-00)

Related Items (7)

Unveiling Talbot Effect under Fresnel Diffraction at a Fork‐Shaped Grating ⋮ On a problem of heat equation with fractional load ⋮ Barnes-Ismagilov integrals and hypergeometric functions of the complex field ⋮ Computation of Mellin convolution integrals with a logarithmic kernel: application to the third Appell function ⋮ The foundations of fractional calculus in the Mellin transform setting with applications ⋮ On an integral related to biaxially anisotropic media ⋮ On Mellin convolution operators: a direct approach to the asymptotic formulae

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• A class of discontinuous integrals involving Bessel functions
• Love's integral and other relations between solutions to mixed boundary-value problems in potential theory
• An Infinite Integral Involving Bessel Functions
• XIII.—Some Integrals, with respect to their Degrees, of Associated Legendre Functions
• The Dual Integral Representations of Kummer's Series ₁ F ₁ (a; c; x )
• Some Definite Integrals of the Product of Two Bessel Functions of the Second Kind: (Order Zero)
• Some Integrals Involving Associated Legendre Functions
• Integrals of Products of Laguerre Polynomials
• Technique for Evaluating Indefinite Integrals Involving Products of Certain Special Functions
• On the Hankel transform of a generalized Laguerre polynomial and on the convolution involving special Bessel functions
• Note on the Integrals of Products of Associated Legendre Functions
• Footnote to the evaluation of certain complex elliptic integrals
• ON SOME FORMULAE FOR INTEGRALS OF ASSOCIATED LEGENDRE FUNCTIONS
• The Laplace Transform of the Modified Bessel Function K(t^±mx) where m = 1, 2, 3, …, n
• Evaluation of Certain Integrals Involving Bessel Functions
• A Note on Evaluation of the Integral
• The Inverse Laplace Transform of the Product of Bessel and Whittaker Functions
• Some infinite integrals involving E-functions
• Some Integral Formulas for the Complete Elliptic Integrals of the First and Second Kind
• Some Special Integrals
• On a Class of Integrals Related to Those of Raabe and Laplace occurring in the theory of Water Waves
• Some Integrals Relating to the I e -Function
• The Incomplete Liouville Multiple Integral and its Application
• Combinatorial Applications of Hermite Polynomials
• A Remarkable Property of Definite Integrals
• Laplace transforms of Airy functions
• Analytical Calculation of a Class of Integrals Containing Exponential and Trigonometric Functions
• A simple proof of a transformation formula for elliptic integrals
• Euler's Integrals
• The Inverse Laplace Transform of the Modified Bessel Function K_mn (a ^1/2m p ^1/2m )
• Numerical Values of Some Integrals involving Bessel Functions
• Some Integrals Occurring in the Theory of Rubber Viscosity
• On Certain Multiple Integrals Occurring in a Waveguide Scattering Problem
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• Ramanujan's Extensions of the Gamma and Beta Functions
• A unified radon inversion formula
• A class of double integrals involving Gaussian and trigonometric factors
• Lattice Green’s functions for cubic lattices
• Moivre's and Fresnel's Integrals by Simple Integration
• On Some Orthogonal Polynomial Integrals
• Representation of Special Functions by Differintegral and Hyperdifferential Operators
• Non-classical integrals of Bessel functions
• Some Basic Hypergeometric Extensions of Integrals of Selberg and Andrews
• Some integrals involving associated Legendre functions and Gegenbauer polynomials
• The Laplace Transform of a Product of Bessel Functions
• Repeating Use of Integral Transforms—A New Method for Evaluation of Some Infinite Integrals
• On Stieltjes Integral Transforms Involving Γ-Functions
• On a simple unified method of deriving recurrence relations among elliptic integrals
• Integrals of Jacobi Functions
• Recurrence Relations for the Indefinite Integrals of the Associated Legendre Functions
• Evaluation of Certain Real Integrals by Contour Integration
• Hypervirial calculation of integrals involving Bessel functions
• Simultaneous Reduction and Expansion of Multidimensional Laplace Transform Kernels
• Complete elliptic integrals resulting from infinite integrals of Bessel functions
• Some integrals involving the&lt;tex&gt;Q_M&lt;/tex&gt;function (Corresp.)
• An Integral Representation for the Product of Two Jacobi Polynomials†
• Concerning $\int _0^\infty e^{ - at} J_\mu (bt)J_\nu (ct)t^{\mu - \nu} dt$
• Further Integrals Involving E-Functions
• An Extension of Schuster's Integral
• A General Theorem in Laplace Transforms
• New Forms of Certain Integrals
• SOME INTEGRALS INVOLVING E-FUNCTIONS AND CONFLUENT HYPERGEOMETRIC FUNCTIONS
• On the repeated integrals of Bessel functions
• On certain infinite integrals involving Struve functions and parabolic cylinder functions
• On certain integrals of Lipschitz-Hankel type involving products of bessel functions
• Spezielle Integrale mit Zylinder‐ und Kugelfunktionen
• Note on an Integral of Ramanujan
• On the evaluation of indefinite integrals involving the special functions: development of method
• On the evaluation of indefinite integrals involving the special functions: application of method
• Integrals for Asymptotic Expansions of Hypergeometric Functions
• Integrals Involving E-Functions and Associated Legendre Functions
• Integrals Involving Products of Modified Bessel Functions of the Second Kind
• THE INTEGRAL OF THE ASSOCIATED LEGENDRE FUNCTION
• On Certain Infinite Integrals Involving Bessel Functions
• Two Integrals involving Modified Bessel Functions of the Second Kind
• Some Results involving Hypergeometric and E-Functions
• NOTE ON THE DEFINITE INTEGRAL OVER PRODUCTS OF THREE LEGENDRE FUNCTIONS
• On Meijer transform
• On the product of two confluent hypergeometric functions
• Integrals involving E-functions
• Integrals involving products of Bessel functions
• Integrals involving E-functions
• Integrals involving a generalized function of two variables
• On the application of transforms for computation of integrals involving Legendre's function
• On the product of two confluent hypergeometric functions
• Integrals involving products of Bessel functions

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