Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Temme, Nico M.
• Is Part Of: Integral transforms and special functions. Volume 33:Issue 1(2022)
• Page Start: 16
• Page End: 31
• Publication Date: 2022-01-02
• Subjects: Asymptotic expansions -- Kummer functions -- confluent hypergeometric functions; Primary 41A60 -- Secondary 33C15; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2021.1886094
• Languages: English
• ISSNs: 1065-2469

Abstract

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.