Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters

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.

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