Applications of the operator H(α,β) to the Humbert double hypergeometric functions

2008/10/21 by A. Hasanov, Anvar Hasanov, Hasanov, A.
Mathematics · Physics and Astronomy · #33C15 #FOS: Mathematics #FOS: Physical sciences #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:33C15

paper · pdf · doi:10.48550/arxiv.0810.3796

11

arxiv created 2008/10/21 · openalex publication_date 2008/10/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Humbert hypergeometric functions Φ₁ , Φ₂ , Φ₃ , Ψ₁ , Ψ₂ , Ξ₁ and Ξ₂ . These operational representations are constructed and applied in order to derive the corresponding decomposition formulas. With the help of these inverse pairs of symbolic operators, a total 34 decomposition formulas are found. Euler type integrals, which are connected with Humbert's functions are found.

Related

• Applications of an operator H(α,β) to the Lauricella multivariable hypergeometric functions
• Decompositions for hypergeometric function H_A, H_B,H_C
• Decomposition formulas associated with the multivariable confluent hypergeometric functions
• Derivatives of Humbert confluent hypergeometric functions with respect to their parameters
• An extension of basic Humbert hypergeometric functions Φ1, Φ2 and Φ3