Results 11 to 20 of about 10,686,469 (301)
Whittaker limits of difference spherical functions [PDF]
International Mathematics Research Notices, 2009 We introduce the (global) q-Whittaker function as the limit at t=0 of the q,t-spherical function extending the symmetric Macdonald polynomials to arbitrary eigenvalues. The construction heavily depends on the technique of the q-Gaussians developed by the
Cherednik, Ivan
core +10 more sources
On $b$-Whittaker functions [PDF]
, 2018 The $b$-Whittaker functions are eigenfunctions of the modular $q$-deformed $\mathfrak{gl}_n$ open Toda system introduced by Kharchev, Lebedev, and Semenov-Tian-Shansky.
Schrader, Gus, Shapiro, Alexander
core +4 more sources
Whittaker's Cardinal Function in Retrospect* [PDF]
Mathematics of Computation, 1971 This paper exposes properties of the Whittaker cardinal function and illustrates the use of this function as a mathematical tool. The cardinal function is derived using the Paley-Wiener theorem. The cardinal function and the central-difference expansions are linked through their similarities.
J. McNamee, F. Stenger, E. Whitney
semanticscholar +2 more sources
Eigenvalues and Whittaker's Function
Nature, 1927 AMONG those who are trying to acquire a general acquaintance with Schrodinger's wave-mechanics there must be many who find their mathematical equipment insufficient to follow his first great problem—to determine the eigenvalues and eigenfunctions for the hydrogen atom. I do not think it is generally realised that Schrodinger's differential equation for
A. Eddington
semanticscholar +2 more sources
A whittaker function of matrix argument
Linear Algebra and its Applications, 1998 Für positiv definite symmetrische \(p\times p\)-Matrizen und für \(\text{Re} (\beta-\alpha)> (p-3)/4\) wird die Whittaker-Funktion \(W_{\alpha,\beta} (A)\) durch folgende Gleichung definiert: \[ \begin{multlined} |A|^{-\beta- (p+1)/4} \Gamma_p(\beta- \alpha+(p+1)/4) e^{\text{tr } A/2} W_{\alpha,\beta}(A)=\\ \int|Z|^{\beta- \alpha-(p+1)/4} |I+Z|^{\alpha+
A. Mathai, G. Pederzoli
semanticscholar +2 more sources
Integral transforms involving a generalized k-Bessel function
Demonstratio Mathematica, 2023 The main goal of this study was to look into some new integral transformations that are associated with a generalized kk-Bessel function. Integral formulas for the generalized kk-Bessel function have been established using the Laplace transform, Euler ...
Khammash Ghazi S. +4 more
doaj +1 more source
AIMS Mathematics, 2020 For two continual bases in the representation space, we obtain the matrix elements of the linear operator transforming the first basis into the second. These elements are expressed in terms of Coulomb wave functions.
I. A. Shilin, Junesang Choi, Jae Won Lee
doaj +1 more source
Uniform asymptotic expansions for the Whittaker functions Mκ,μ(z) and Wκ,μ(z) with μ large [PDF]
Proceedings of the Royal Society A, 2021 Uniform asymptotic expansions are derived for Whittaker’s confluent hypergeometric functions Mκ,μ(z) and Wκ,μ(z), as well as the numerically satisfactory companion function W−κ,μ(z e−πi).
T. M. Dunster
semanticscholar +1 more source
Axioms, 2023 In this paper, first derivatives of the Whittaker function Mκ,μx are calculated with respect to the parameters. Using the confluent hypergeometric function, these derivarives can be expressed as infinite sums of quotients of the digamma and gamma ...
Alexander Apelblat +1 more
doaj +1 more source
WHITTAKER FUNCTIONS AND DEMAZURE CHARACTERS [PDF]
Journal of the Institute of Mathematics of Jussieu, 2017 In this paper, we consider how to express an Iwahori–Whittaker function through Demazure characters. Under some interesting combinatorial conditions, we obtain an explicit formula and thereby a generalization of the Casselman–Shalika formula. Under the same conditions, we compute the transition matrix between two natural bases for the space of Iwahori ...
Lee, Kyu-Hwan +2 more
openaire +1 more source