Irrationality exponents of certain alternating series.

Let m be a positive integer, (w n) be a sequence of positive integers, and (y n) be a sequence of nonzero integers with y 1 ≥ 1 . Define q 0 = 1 , q 1 = w 0 , q n + 1 = q n - 1 (w n q n m + y n) (n ≥ 1) . Under certain assumptions on (w n) and (y n) , we give the exact value of the irrationality exponent of the number ξ = ∑ n = 1 ∞ (- 1) n - 1 y 1 y 2 ⋯ y n q n q n - 1 . [ABSTRACT FROM AUTHOR]