ABSTRACT
New asymptotic expansions are derived of the Kummer functions and for large positive values of a and b, with z fixed. For both functions we consider and , with special attention for the case . We use a uniform method to handle all cases of these parameters.
2010 Mathematics Subject Classifications:
Acknowledgments
The author is grateful to the reviewer for careful reading earlier versions of the manuscript and for helpful comments that improved the article. The author thanks CWI, Amsterdam, for scientific support.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 This follows from the first functions given in (EquationA14(A14) (A14) ) and induction with respect to n.
2 The reviewer observed: It seems that the numerical coefficients are the same as the sequence A269940 in the OEIS. It would be worth investigating this in the future. See also https://oeis.org/A269940.