Logarithmic derivative of the Euler Γ function in Clifford analysis.

Guy Laville; Louis Randriamihamison

Revista Matemática Iberoamericana (2005)

  • Volume: 21, Issue: 3, page 695-728
  • ISSN: 0213-2230

Abstract

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The logarithmic derivative of the Γ-function, namely the ψ-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 ψ-function. These new functions show links between well-known constants: the Eurler gamma constant and some generalisations, ζR(2), ζR(3). We get also the Riemann zeta function and the Epstein zeta functions.

How to cite

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Laville, Guy, and Randriamihamison, Louis. "Logarithmic derivative of the Euler Γ function in Clifford analysis.." Revista Matemática Iberoamericana 21.3 (2005): 695-728. <http://eudml.org/doc/41947>.

@article{Laville2005,
abstract = {The logarithmic derivative of the Γ-function, namely the ψ-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 ψ-function. These new functions show links between well-known constants: the Eurler gamma constant and some generalisations, ζR(2), ζR(3). We get also the Riemann zeta function and the Epstein zeta functions.},
author = {Laville, Guy, Randriamihamison, Louis},
journal = {Revista Matemática Iberoamericana},
keywords = {Funciones especiales; Función gamma; Función zeta; Algebras de Clifford; Clifford analysis; special functions; Gamma function; Zeta function},
language = {eng},
number = {3},
pages = {695-728},
title = {Logarithmic derivative of the Euler Γ function in Clifford analysis.},
url = {http://eudml.org/doc/41947},
volume = {21},
year = {2005},
}

TY - JOUR
AU - Laville, Guy
AU - Randriamihamison, Louis
TI - Logarithmic derivative of the Euler Γ function in Clifford analysis.
JO - Revista Matemática Iberoamericana
PY - 2005
VL - 21
IS - 3
SP - 695
EP - 728
AB - The logarithmic derivative of the Γ-function, namely the ψ-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 ψ-function. These new functions show links between well-known constants: the Eurler gamma constant and some generalisations, ζR(2), ζR(3). We get also the Riemann zeta function and the Epstein zeta functions.
LA - eng
KW - Funciones especiales; Función gamma; Función zeta; Algebras de Clifford; Clifford analysis; special functions; Gamma function; Zeta function
UR - http://eudml.org/doc/41947
ER -

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