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December, 2005 Logarithmic derivative of the Euler $\Gamma$-function in Clifford analysis
Guy Laville, Louis Randriamihamison
Rev. Mat. Iberoamericana 21(3): 695-728 (December, 2005).

Abstract

The logarithmic derivative of the $\Gamma$-function, namely the $\psi$-function, has numerous applications. We define analogous functions in a four dimensional space. We cut lattices and obtain Clifford-valued functions. These functions are holomorphic cliffordian and have similar properties as the $\psi$-function. These new functions show links between well-known constants: the Euler gamma constant and some generalisations, $\zeta^R(2)$, $\zeta^R(3)$. We get also the Riemann zeta function and the Epstein zeta functions.

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Guy Laville. Louis Randriamihamison. "Logarithmic derivative of the Euler $\Gamma$-function in Clifford analysis." Rev. Mat. Iberoamericana 21 (3) 695 - 728, December, 2005.

Information

Published: December, 2005
First available in Project Euclid: 11 January 2006

zbMATH: 1103.30032
MathSciNet: MR2231008

Subjects:
Primary: 30G35‎ , 31B30 , 33B15

Keywords: $\psi$-function , Clifford analysis , dilogarithm function , Euler constant , Non-commutative analysis

Rights: Copyright © 2005 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.21 • No. 3 • December, 2005
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