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.
@article{1136999129,
author = {Laville, Guy and Randriamihamison, Louis},
title = {Logarithmic derivative of the Euler $\Gamma$-function in Clifford analysis},
journal = {Rev. Mat. Iberoamericana},
volume = {21},
number = {2},
year = {2005},
pages = { 695-728},
language = {en},
url = {http://dml.mathdoc.fr/item/1136999129}
}
Laville, Guy; Randriamihamison, Louis. Logarithmic derivative of the Euler $\Gamma$-function in Clifford analysis. Rev. Mat. Iberoamericana, Tome 21 (2005) no. 2, pp. 695-728. http://gdmltest.u-ga.fr/item/1136999129/