Results 191 to 200 of about 33,268 (232)

Integrals involving products of generalized Whittaker functions

Mathematical Proceedings of the Cambridge Philosophical Society, 1965
In ((4)) Slater gave expansions of the generalized Whittaker functons pFp(x). (She gave this name to the generalized hypergeometric function pFp(x), since it is a generalization of the well-known Whittaker function 1F1(x).) In another paper ((2)), Ragab gave a series of products of generalized Whittaker functions in terms of such functions or in terms ...
Ragab, F. M., Simary, M. A.
openaire   +2 more sources

An Integral Transform Involving the Product Of Bessel Functions and Whittaker Function and Its Application

International Journal of Applied and Computational Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Belafhal, E. M. El Halba, T. Usman
openaire   +2 more sources

Integrals involving Whittaker functions

Annali di Matematica Pura ed Applicata, 1964
Integrals involving products of two Whittaker functions and Bessel functions are evaluated in §§ 3, 4. Also the integrals Open image in new window are evaluated in § 5 while in § 6 integrals involving the product of three Whittaker functions are established.
openaire   +2 more sources

Certain integral representations for Whittaker functions

Mathematical Proceedings of the Cambridge Philosophical Society, 1948
1. Shastri (1) has shown that if and thenBut (Goldstein (2))hence substituting from (1·2) in (1·1) and changing the order of integration, which we suppose to be permissible, we find that ifthenassuming of course that the integrals converge.
openaire   +2 more sources

An integral involving Fox's H-function and Whittaker functions

Mathematical Proceedings of the Cambridge Philosophical Society, 1969
1. In this paper we have evaluated an integral involving Fox's H-functions and Whittaker functions. One particular case of the integral has been employed to establish an expansion formula for the H-function involving Laguerre polynomials.
openaire   +2 more sources

Double SO(2, 1)-integrals and formulas for Whittaker functions

Russian Mathematics, 2012
The relation \[ [T_\sigma (g)](u(x))=u(g^{-1}x) \] defines a representation of \(SO(2,1)\) in the space \(D_\sigma \) of infinitely differentiable functions \(f\) on the cone \(x_0^2-x_1^2-x_2^2=0\) and satisfying the homogeneity condition \(f(\alpha x)=\alpha ^\sigma f(x)\). By using the circle \(\gamma _1: x_1^2+x_2^2=1\), the hyperbola \(x_0^2-x_2^2=
openaire   +2 more sources

INTEGRAL RELATIONS FOR THE WHITTAKER FUNCTIONS AND THE REPRESENTATIONS OF THE THREE-DIMENSIONAL LORENTZ GROUP

Mathematics of the USSR-Sbornik, 1970
We construct elements of the matrix which connects different bases for class I representations of the group SO(2,1). These matrix elements are expressed in terms of Whittaker functions. In this way integral relations are obtained for these and orhte special functions. Bibliography: 5 items.
Vilenkin, N. Ya., Shlejnikova, M. A.
openaire   +1 more source

LXXV.Integral representations for products of Whittaker functions

The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1938
(1938). LXXV. Integral representations for products of Whittaker functions. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 26, No. 178, pp. 871-877.
openaire   +1 more source

Infinite integrals of Whittaker and Bessel functions with respect to their indices

Journal of Mathematical Physics, 2009
We obtain several new closed-form expressions for the evaluation of a family of infinite-domain integrals of the Whittaker functions Wκ,μ(x) and Mκ,μ(x) and the modified Bessel functions Iμ(x) and Kμ(x) with respect to the index μ. The new family of definite integrals is useful in a variety of contexts in mathematical physics.
openaire   +1 more source

Some infinite integrals involving Whittaker functions and generalized hypergeometric polynomials, with their applications

Mathematical Proceedings of the Cambridge Philosophical Society, 1969
We have defined the generalized hypergeometric polynomial ((6), eqn. (2·1), p. 79) by means ofwhere δ and n are positive integers and the symbol Δ(δ, − n) represents the set of δ-parametersThe polynomial is in a generalized form which yields many known polynomials with proper choice of parameters and therefore the results are of general character.
openaire   +2 more sources