Some decomposition formulas of generalized hypergeometric functions and formulas of an analytic continuation of the Clausen function

2008/10/15 by A. Hasanov, Anvar Hasanov, Hasanov, A.
Chemistry · Mathematics · Physics and Astronomy · #33C20 #Algebra over a field #Analytic continuation #Analytic function #Applied mathematics #Basic hypergeometric series #Chemistry #Classical Analysis and ODEs (math.CA) #Computer science #Confluent hypergeometric function #Continuation #Decomposition #FOS: Mathematics #FOS: Physical sciences #Function (biology) #Generalized hypergeometric function #Hypergeometric function #Hypergeometric function of a matrix argument #Lauricella hypergeometric series #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Pure mathematics #math-ph #math.CA #math.MP #msc:33C20

paper · pdf · doi:10.48550/arxiv.0810.2636

published in arXiv (Cornell University) (Cornell University) · 9 pages

arxiv created 2008/10/15 · openalex publication_date 2008/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, using similar symbolical method of Burchnall and Chaundy formulas of expansion for the generalized hypergeometric function were constructed. By means of the found formulas of expansion the formulas of an analytic continuation for hypergeometric function of Clausen is defined. The obtained formulas of an analytic continuation express known hypergeometric Appell function F₂ (a;b₁, b₂ ;c₁, c₂ ;x,y) which theory is well studied.

Related

• Tables of the Appell Hypergeometric Functions F₂
• Decompositions for hypergeometric function H_A, H_B,H_C
• On the Connection between Generalized Hypergeometric Functions and Dilogarithms
• The Appell hypergeometric expansions of the solutions of the general Heun equation
• Some summation theorems for Clausen's hypergeometric functions with unit argument