Resumen de On the transcendence of some infinite sums

Pingzhi Yuan, Juan Li

• 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.