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A Quadruple Integral Containing the Gegenbauer Polynomial Cn(λ)(x): Derivation and Evaluation
- Source :
- Symmetry, Vol 14, Iss 2, p 205 (2022)
- Publication Year :
- 2022
- Publisher :
- MDPI AG, 2022.
-
Abstract
- A four-dimensional integral containing g(x,y,z,t)Cn(λ)(x) is derived. Cn(λ)(x) is the Gegenbauer polynomial, g(x,y,z,t) is a product of the generalized logarithm quotient functions and the integral is taken over the region 0≤x≤1,0≤y≤1,0≤z≤1,0≤t≤1. The integral is difficult to compute in general. Special cases are given and invariant index forms are derived. The zero distribution of almost all Hurwitz–Lerch zeta functions is asymmetrical. All the results in this work are new.
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 14
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Symmetry
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.94ba0486f6ae4687a1bfce0159b242de
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/sym14020205