Linear independence of values of some hypergeometric functions
type: Item
instance of: scholarly article
title: Linear independence of values of some hypergeometric functions
zbMATH Open document ID: 0591.10024
author: O. N. Vasilenko
published in: Moscow University Mathematics Bulletin
publication date: 1985-01-01T00:00:00Z
review text: Let us define \[ F(\alpha +1,1,\gamma +1;z)=\sum^{\infty}_{r=0}\frac{(\alpha +1)...(\alpha +r)}{(\gamma +1)...(\quad \gamma +r)}z^ r,\quad \alpha,\gamma \in {\mathbb{Q}},\quad \gamma \neq -1,-2,.... \] Further, let \(f_ i(z)=F(\alpha +1,1,\gamma +1;z_ iz)\), \(i=1,...,s\), where \(z_ 1,...,z_ s\) are non-zero rational numbers satisfying \(z_ i\neq z_ j\), \(\forall i\neq j\). Using the results of \textit{Yu. V. Nesterenko} [Vestn. Mosk. Univ., Ser. I 1985, No.1, 46-49 (1985; Zbl 0572.10027)] the author obtains sharp explicit estimates for linear forms \[ | x_ 0+x_ 1 f_ 1(z)+...+x_ s f_ s(z)|,\quad x_ i\in {\mathbb{Z}}, \] at certain rational points z.
Mathematics Subject Classification ID: 11J81
Mathematics Subject Classification ID: 33C60
zbMATH DE Number: 3948383
zbMATH Keywords: Pade approximations
zbMATH Keywords: measure of linear independence
zbMATH Keywords: values of
zbMATH Keywords: hypergeometric Gauss function
zbMATH Keywords: irrationality
zbMATH Keywords: explicit estimates
zbMATH Keywords: linear forms
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3948383