Irrationality results for two particular functions. (Des résultats d’irrationalité pour deux fonctions particulières.) (French) Zbl 1159.11316

Choulet, Richard

Collect. Math. 52, No. 1, 1-20 (2001).

Summary: This paper studies irrationality of values taken by the functions \(T_q\) defined by \(T_q(z)=\sum^{+\infty}_{n=0}z^n/q^{n(n+1)/2}\), and \(E_q\) such that \(E_q(z)=\sum^{+\infty}_{n=0}z^n/\prod^n_{k=1}(q^k-1)\), where \(q\in\mathbb Q\) and \(|q|>1\).

MSC:

11J72	Irrationality; linear independence over a field
11J91	Transcendence theory of other special functions

Keywords:

Tschakaloff function; \(q\)-analog of exponential function; irrationality