An orthogonality relation for the Whittaker functions of the second kind of imaginary order

DOI10.1080/10652461003643412zbMath1205.33010arXiv0910.1492OpenAlexW2089448682MaRDI QIDQ3053701

Radosław Szmytkowski, Sebastian Bielski

Publication date: 29 October 2010

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.1492

zbMATH Keywords

orthogonal functionsWhittaker functionsDirac delta distributionConfluent hypergeometric functions

Mathematics Subject Classification ID

Other special orthogonal polynomials and functions (33C47) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

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Comment on the orthogonality of the Macdonald functions of imaginary order ⋮ An analytic expression for the distribution of the generalized Shiryaev-Roberts diffusion. The Fourier spectral expansion approach ⋮ Symmetries and spectral statistics in chaotic conformal field theories ⋮ Complexity via replica trick ⋮ Harnessing S-duality in \(\mathcal{N} = 4\) SYM \& supergravity as \(\mathrm{SL}(2, \mathbb{Z})\)-averaged strings ⋮ Casimir energy and modularity in higher-dimensional conformal field theories ⋮ On quantum complexity ⋮ On the evaluation of an integral involving the Whittaker \(W\) function ⋮ Harmonic analysis of 2d CFT partition functions ⋮ A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices ⋮ Time-dependent probability density function for general stochastic logistic population model with harvesting effort ⋮ Orthogonality relations for the associated Legendre functions of imaginary order

Cites Work

• Unnamed Item
• Comment on the orthogonality of the Macdonald functions of imaginary order
• On the orthogonality of the MacDonald's functions
• Index transforms associated with products of Whittaker's functions
• On the integration of products of Whittaker functions with respect to the second index
• A Class of Integral Transforms
• The Confluent Hypergeometric Function

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