Padé Approximations and Irrationality Measures on Values of Confluent Hypergeometric Functions.

Padé approximations are approximations of holomorphic functions by rational functions. The application of Padé approximations to Diophantine approximations has a long history dating back to Hermite. In this paper, we use the Maier–Chudnovsky construction of Padé-type approximation to study irrationality properties about values of functions with the form f (x) = ∑ k = 0 ∞ x k k ! (b k + s) (b k + s + 1) ⋯ (b k + t) , where b , t , s are positive integers and obtain upper bounds for irrationality measures of their values at nonzero rational points. Important examples includes exponential integral, Gauss error function and Kummer's confluent hypergeometric functions. [ABSTRACT FROM AUTHOR]