JournalsrmiVol. 21, No. 3pp. 695–728

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

  • Guy Laville

    Université de Caen, Caen, France
  • Louis Randriamihamison

    Institut National Polytechnique de Toulouse, Toulouse, France
Logarithmic derivative of the Euler $\Gamma$-function in Clifford analysis cover
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Abstract

The logarithmic derivative of the Γ\Gamma-function, namely the ψ\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 ψ\psi-function. These new functions show links between well-known constants: the Euler gamma constant and some generalisations, ζR(2)\zeta^R(2), ζR(3)\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 Γ\Gamma-function in Clifford analysis. Rev. Mat. Iberoam. 21 (2005), no. 3, pp. 695–728

DOI 10.4171/RMI/433