Some integral representations and limits for (products of) the parabolic cylinder function

DOI10.1080/10652469.2015.1092441zbMath1347.33010arXiv1505.01948OpenAlexW3101620097MaRDI QIDQ2790231

Dirk Veestraeten

Publication date: 3 March 2016

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

Full work available at URL: https://arxiv.org/abs/1505.01948

zbMATH Keywords

gamma functionlimitsOrnstein-Uhlenbeck processintegral representationsmodified Bessel functionparabolic cylinder function

Mathematics Subject Classification ID

Diffusion processes (60J60) Laplace transform (44A10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (4)

An integral representation for the product of two parabolic cylinder functions having unrelated arguments ⋮ Lebedev identities and integral representations of products of Hermite functions ⋮ An integral representation for the product of parabolic cylinder functions ⋮ Some Laplace transforms and integral representations for parabolic cylinder functions and error functions

Cites Work

• An integral representation for the product of two parabolic cylinder functions having unrelated arguments
• On the inverse transform of Laplace transforms that contain (products of) the parabolic cylinder function
• A Nicholson-Type Integral for the Product of Two Parabolic Cylinder Functions D ν ( x ) D ν (− x ) AT ℜν≪0
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