Year: 2018
Type: article
Abstract: The question was asked: Is it possible to express the function h(a) ≡ 4 F 3 (a,a,a,a;2a,a + 1, a + 1; 1)(1.1) in closed form [1]? After considerable analysis, the answer appears to be "no", but during the attempt to answer this question, a number of interesting (and unexpected) related results were obtained, either as specialized transformations, or as closed-form expressions for several related functions.The purpose of this paper is to record and review both the methods attempted and the related identities obtained, the former for their educational merit, the latter because they do not appear to exist in the literature.Specifically, new 4 F 3 (1) , 5 F 6 (1) and generalized Euler sums (those containing digamma functions) are presented along with a detailed discussion of the methods used to obtain them.
Source: Journal of Classical Analysis
Author: Michael Milgram
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2791405334