Generalized Hölder's Theorem for Vignéras' Multiple Gamma Function

NISHIZAWA, Michitomo

Tokyo J. of Math., Tome 24 (2001) no. 2, p. 323-329 / Harvested from Project Euclid

Résumé

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.

Publié le : 2001-06-15
Classification:

@article{1255958332,
     author = {NISHIZAWA, Michitomo},
     title = {Generalized H\"older's Theorem for Vign\'eras' Multiple Gamma Function},
     journal = {Tokyo J. of Math.},
     volume = {24},
     number = {2},
     year = {2001},
     pages = { 323-329},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255958332}
}

NISHIZAWA, Michitomo. Generalized Hölder's Theorem for Vignéras' Multiple Gamma Function. Tokyo J. of Math., Tome 24 (2001) no. 2, pp.  323-329. http://gdmltest.u-ga.fr/item/1255958332/