A Nicholson-Type Integral for the Product of Two Parabolic Cylinder Functions D ν ( x ) D ν (− x ) AT ℜν≪0

DOI10.1080/1065246031000074371zbMath1037.33007arXivmath/0106142OpenAlexW3103575037MaRDI QIDQ4409778

Cyril Malyshev

Publication date: 30 June 2003

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

Full work available at URL: https://arxiv.org/abs/math/0106142

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (7)

An integral representation for the product of two parabolic cylinder functions having unrelated arguments ⋮ Lebedev identities and integral representations of products of Hermite functions ⋮ A quadruple integral involving the product of generalized parabolic cylinder functions 𝐷ᵥ(𝛽𝑥)𝐷ᵤ(𝛼𝑧): Derivation and evaluation ⋮ Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side ⋮ An integral representation for the product of parabolic cylinder functions ⋮ Some integral representations and limits for (products of) the parabolic cylinder function ⋮ Product of parabolic cylinder functions involving Laplace transforms of confluent hypergeometric functions

Cites Work

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• Inequalities and monotonicity properties for zeros of Hermite functions
• On the squares of Weber's parabolic cylinder functions and certain integrals connected with them
• On the Product of Parabolic Cylinder Functions with Different Arguments
• EINIGE INTEGRALDARSTELLTUNGEN FÜR PRODUKTE VON WHITTAKERSCHEN FUNKTIONEN
• AN INTEGRAL REPRESENTATION FOR THE PRODUCT OF TWO WHITTAKER FUNCTIONS
• EXPANSIONS AND INTEGRAL-TRANSFORMS FOR PRODUCTS OF LAGUERRE AND HERMITE POLYNOMIALS

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