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

### Guy Laville

Université de Caen, Caen, France### Louis Randriamihamison

Institut National Polytechnique de Toulouse, Toulouse, France

## 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.

## Cite this article

Guy Laville, Louis Randriamihamison, Logarithmic derivative of the Euler $\Gamma$-function in Clifford analysis. Rev. Mat. Iberoam. 21 (2005), no. 3, pp. 695–728

DOI 10.4171/RMI/433