On the transcendence of some infinite sums

Autores: Pingzhi Yuan, Juan Li
Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 2, 2009, págs. 431-445
Idioma: inglés
DOI: 10.1112/jlms/jdp029
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Resumen
- In this paper we investigate the infinite convergent sum T = �� n=0 P(n)/Q(n), where P(x) �¸ Q[x] and Q(x) �¸ Q[x], and Q(x) has only simple rational zeros. N. Saradha and R.
  
  Tijdeman have obtained sufficient and necessary conditions for the transcendence of T if the degree of Q(x) is 3. In this paper we give sufficient and necessary conditions for the transcendence of T if the degree of Q(x) is 4 and Q(x) is reduced.