## Abstract

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 ψ_{2} . 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 language | English |
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Article number | 868 |

Journal | Symmetry |

Volume | 14 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2022 |

Externally published | Yes |

## Keywords

- 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)

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