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June 2001 Generalized Hölder's Theorem for Vignéras' Multiple Gamma Function
Tokyo J. Math. 24(1): 323-329 (June 2001). DOI: 10.3836/tjm/1255958332


We prove that Vignéras' multiple gamma function does not satisfy any algebraic differential equation over $\mathbf{C}(z)$ by using a relation between logarithmic derivative of this function and the psi-function. Furthermore, we apply this relation to calculation of convergent factors in the Weierstrass product representation of Vignéras' multiple gamma function.


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Michitomo NISHIZAWA. "Generalized Hölder's Theorem for Vignéras' Multiple Gamma Function." Tokyo J. Math. 24 (1) 323 - 329, June 2001.


Published: June 2001
First available in Project Euclid: 19 October 2009

zbMATH: 1009.33002
MathSciNet: MR1844438
Digital Object Identifier: 10.3836/tjm/1255958332

Rights: Copyright © 2001 Publication Committee for the Tokyo Journal of Mathematics

Vol.24 • No. 1 • June 2001
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