On the irrationality of Σ tn/Aan+Bβn

[摘要] In Andre-Jeannin's article (C.R. Acad. Sci. Paris Ser. I. 308(19), 539-541), he proved the irrationality of f(x) := Sigma x(n)/w(n) where x is an integer in the disk of convergence of the series f and (w(n))(n) a second order recurring sequence of ntegers. In this paper using the three terms recurrence relations between formal orthogonal polynomials we extend the result of Andre-Jeannin to any rational x in the domain of meromorphy of f: Moreover, for particular sequences w(n) we find an irrationality measure for f(x). (C) 1998 Academic Press.

[发布日期] 1998-12-01