A Quadruple Integral Involving Chebyshev Polynomials <i>T<sub>n</sub></i>(<i>x</i>): Derivation and Evaluation

A Quadruple Integral Involving Chebyshev Polynomials <i>T<sub>n</sub></i>(<i>x</i>): Derivation and Evaluation

The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi>&l...

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Bibliographic Details
Main Authors: Robert Reynolds, Allan Stauffer
Format: Article
Language:English
Published: MDPI AG 2022-01-01
Series:Symmetry
Subjects:
Chebyshev polynomial
quadruple integral
Hurwitz-Lerch zeta function
Apéry’s constant
Online Access:https://www.mdpi.com/2073-8994/14/1/100
Description
Summary:The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi><mi>n</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and derive in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. The zero distribution of almost all Hurwitz-Lerch zeta functions is asymmetrical. All the results in this work are new.
ISSN:2073-8994

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