On the properties of the (p,ν)-extension of the Whittaker function M_κ,μ(z)

2018/01/30 by Showkat Ahmad Dar, S A Dar, Dar, S A +3
Mathematics · #33A22 #33B15 #33C05 #33C10 #33C15 #33C45 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #math.CA #msc:33A22 #msc:33B15 #msc:33C05 #msc:33C10 #msc:33C15 #msc:33C45

paper · pdf · doi:10.48550/arxiv.1801.09921

11 pages, 0 figures

arxiv created 2018/01/30 · openalex publication_date 2018/01/30 · arxiv updated 2018/01/31 · openalex created_date 2018/02/23 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain a (p,ν)-extension of the Whittaker function M_κ,μ(z) by using the extended confluent hypergeometric function of the first kind Φ_p,ν(b;c;z) introduced in Parmar et al. [J. Classical Anal. 11 (2017) 81--106]. Also, we derive some of the main properties of this function, namely several integral representations, a summation formula, the analogue of Kummer's transformation formula, an asymptotic representation, the Mellin transform, a differential formula and some inequalities.

Related

• An extension of the Whittaker function
• (p,q)-Whittaker function and associated properties and formulas
• On some identities for confluent hypergeometric functions and Bessel functions
• On an extension of extended Beta and hypergeometric functions
• The modulus of Whittaker functions