Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters. Issue 1 (2nd January 2022) - Temme, Nico M.
ABSTRACT: New asymptotic expansions are derived of the Kummer functions M ( a, b, z ) and U ( a, b + 1, z ) for large positive values of a and b, with z fixed. For both functions we consider b / a ≤ 1 and b / a ≥ 1, with special attention for the case a ∼ b . We use a uniform method to handle all cases of these parameters.