2009/10/01 by Ilia D. Mishev, Mishev, Ilia D.
Chemistry · Mathematics · #33C20 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Molecular spectroscopy and chirality #math.CA #msc:33C20
paper · pdf · doi:10.48550/arxiv.0910.0093
15 pages
arxiv created 2009/10/01 · openalex publication_date 2009/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explore a function L(x)=L(a,b,c,d;e;f,g) which is a linear combination of two Saalschützian 4F3(1) hypergeometric series. We demonstrate a fundamental two-term relation satisfied by the L function and show that the fundamental two-term relation implies that the Coxeter group W(D5), which has 1920 elements, is an invariance group for L(x). The invariance relations for L(x) are classified into six types based on a double coset decomposition of the invariance group. The fundamental two-term relation is shown to generalize classical results about hypergeometric series. We derive Thomae's identity for 3F2(1) series, Bailey's identity for terminating Saalschützian 4F3(1) series, and Barnes' second lemma as consequences of the fundamental two-term relation.