PORTUGALIAE MATHEMATICA Vol. 53, No. 2, pp. 229237 (1996) 

A Criterion of IrrationalityDaniel Duverney24 Place du Concert,59800 Lille  FRANCE Abstract: We generalize P. Gordan's proof of the transcendence of $e$ ([3]; [5], p. 170), and obtain a criterion of irrationality (Theorem 1 below). Using this criterion, we can prove the irrationality of $f(z)=1+\sum_{n=1}^{+\infty}\frac{z^{n}}{v_{1}\,v_{2}\cdots v_{n}\,q^{n(n+1)/2}}$, when $z$, $q$ and $v_{n}$ satisfy suitable hypotheses (see Theorem 2). Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1996 Sociedade Portuguesa de Matemática
