Special polynomials and elliptic integrals
type: Item
instance of: scholarly article
title: Special polynomials and elliptic integrals
zbMATH Open document ID: 1222.33005
author: D. Babusci
author: G. Dattoli
published in: Applied Mathematics Letters
publication date: 2011-05-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/0911.2098
review text: The authors show that the use of generalized multivariable forms of Hermite polynomials provide a useful tool for the evaluation of families of integrals often encountered in electrostatics and electrodynamics. The definite integral in (1) can be rewritten as \[ F=\frac{1}{\sqrt{a}}\int_1^{\infty}\frac{dt} {t^{\nu}\sqrt{t-1}}, \] which is not an elliptic integral. The formula in (2) does not use the conventional notation for Laplace transforms. Formula (2) is also false, since it is only valid for integers \(\nu\).
reviewed by: Thomas Ernst
Mathematics Subject Classification ID: 33B99
zbMATH DE Number: 5883268
zbMATH Keywords: elliptic integral
zbMATH Keywords: gamma function
zbMATH Keywords: Hermite polynomials
zbMATH Keywords: Euler function
zbMATH Keywords: Laplace transform
MaRDI profile type: Publication
OpenAlex ID: W2963824627
arXiv ID: 0911.2098
cites work: Q4092387
cites work: Operational rules and arbitrary order Hermite generating functions
cites work: Q3844537
cites work: Q3412707
cites work: Q3215519
DOI: 10.1016/J.AML.2011.01.035
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description: scientific article