Abstract :
In André-Jeanninʹs article (C.R. Acad. Sci. Paris Sér. I.308(19), 539–541), he proved the irrationality off(x)colon, equals∑ xn/wn, wherexis an integer in the disk of convergence of the seriesfand (wn)na second order recurring sequence of integers. In this paper using the three terms recurrence relations between formal orthogonal polynomials we extend the result of André-Jeannin to any rationalxin the domain of meromorphy off. Moreover, for particular sequenceswn, we find an irrationality measure forf(x).
