Revista Matemática Iberoamericana

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Volume 21, Issue 3, 2005, pp. 695–728
DOI: 10.4171/RMI/433

Published online: 2005-12-31

Logarithmic derivative of the Euler $\Gamma$-function in Clifford analysis

Guy Laville[1] and Louis Randriamihamison[2]

(1) Université de Caen, Caen, France
(2) Institut National Polytechnique de Toulouse, Toulouse, France

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.

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

Laville Guy, Randriamihamison Louis: Logarithmic derivative of the Euler $\Gamma$-function in Clifford analysis. Rev. Mat. Iberoam. 21 (2005), 695-728. doi: 10.4171/RMI/433