Another Method for Proving Certain Reduction Formulas for the Humbert Function ψ2 Due to Brychkov et al. with an Application

Asmaa O. Mohammed, Adem Kilicman*, Mohamed M. Awad, Arjun K. Rathie, Medhat A. Rakha

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Recently, Brychkov et al. established several new and interesting reduction formulas for the Humbert functions (the confluent hypergeometric functions of two variables). The primary objective of this study was to provide an alternative and simple approach for proving four reduction formulas for the Humbert function ψ2 . We construct intriguing series comprising the product of two confluent hypergeometric functions as an application. Numerous intriguing new and previously known outcomes are also achieved as specific instances of our primary discoveries. It is well-known that the hypergeometric functions in one and two variables and their confluent forms occur naturally in a wide variety of problems in applied mathematics, statistics, operations research, physics (theoretical and mathematical) and engineering mathematics, so the results established in this paper may be potentially useful in the above fields. Symmetry arises spontaneously in the abovementioned functions.

Original languageEnglish
Article number868
Issue number5
Publication statusPublished - May 2022
Externally publishedYes


  • Ap-pell’s functions
  • confluent hypergeometric function
  • Humbert functions
  • hypergeometric function
  • integral representation
  • reduction formula

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

Cite this