2008/09/30 by Jonathan Murley, Nasser Saad, Murley, Jonathan +1
Mathematics · Physics and Astronomy · #33B15 #33C05 #33C20 #33C65 #33D15 #33D60 #33D90. #Advanced Mathematical Identities #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.0809.5203
openalex publication_date 2008/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The generalized hypergeometric function qFp is a power series in which the ratio of successive terms is a rational function of the summation index. The Gaussian hypergeometric functions 2F1 and 3F2 are most common special cases of the generalized hypergeometric function qFp. The Appell hypergeometric functions Fq, q=1,2,3,4 are product of two hypergeometric functions 2F1 that appear in many areas of mathematical physics. Here, we are interested in the Appell hypergeometric function F2 which is known to have a double integral representation. As demonstrated by Opps, Saad, and Srivastava (J. Math. Anal. Appl. 302 (2005) 180-195), the double integral representation of F2 can be reduced to a single integral that can be easily evaluated for certain values of the parameters in terms of 2F1 and 3F2. Using many of the reduction formulas of 2F1 and 3F2 and the representation of F2 in terms of a single integral, we have begun to tabulate new reduction formulas for F2.