The Cauchy–Schlömilch transformation

DOI10.1080/10652469.2019.1637432zbMath1458.33004arXiv1004.2445OpenAlexW2963935736MaRDI QIDQ5197978

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Publication date: 2 October 2019

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

Full work available at URL: https://arxiv.org/abs/1004.2445

zbMATH Keywords

error functionRiemann zeta functiontransformationsBessel functionelliptic integralsdefinite integralsLaplace integral

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Elliptic functions and integrals (33E05) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (4)

Legendre hyperelliptic integrals, \(\pi\) new formulae and Lauricella functions through the elliptic singular moduli ⋮ Global-local mixtures: a unifying framework ⋮ Hypergeometric identities related to Roberts reductions of hyperelliptic integrals ⋮ From sequences to polynomials and back, via operator orderings

Cites Work

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• Distributions generated by transformation of scale using an extended Cauchy-schlömilch transformation
• Elliptic functions and applications
• IG-symmetry and R-symmetry: Interrelations and applications to the inverse Gaussian theory
• Probabilistic Applications of the Schlömilch Transformation
• A Remarkable Property of Definite Integrals
• An Integral with Three Parameters
• Asymmetry and Gradient Asymmetry Functions: Density‐Based Skewness and Kurtosis
• An integral with three parameters. II

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