A Quadruple Integral Involving Chebyshev Polynomials Tn(x): Derivation and Evaluation

A Quadruple Integral Involving Chebyshev Polynomials Tn(x): Derivation and Evaluation

The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind Tn(x) 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...

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Veröffentlicht in:Symmetry (Basel) 2022-01, Vol.14 (1), p.100
Hauptverfasser: Reynolds, Robert, Stauffer, Allan
Format: Artikel
Sprache:eng
Schlagworte:
Apéry’s constant
Chebyshev approximation
Chebyshev polynomial
Hurwitz-Lerch zeta function
Integrals
Mathematical analysis
Polynomials
quadruple integral
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Zusammenfassung:The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind Tn(x) 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
2073-8994
DOI:10.3390/sym14010100