Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 53, No. 2, pp. 229-237 (1996)

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A Criterion of Irrationality

Daniel Duverney

24 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).

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