A note on a further extension of Gauss's second summation theorem with an application to the extension of two well-known combinatorial identities

Autor:	Gradimir V. Milovanović, Arjun K. Rathie, Insuk Kim, Richard B. Paris
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	Algebra Mathematics (miscellaneous) Gauss Computer Science::Symbolic Computation Extension (predicate logic) Knuth's old sum Reed Dawson identity Riordan identity Gauss second summation theorem hypergeometric summation formulas and identities Mathematics
Zdroj:	Quaestiones Mathematicae; Vol. 45 No. 6 (2022); 959–968
ISSN:	1607-3606 1727-933X
Popis:	Recently, Masjed-Jamei and Koepf established the extension of several classical summation theorems (including Gauss's second summation theorem). Our aim in this paper is to establish a further extension of Gauss's second summation formulas due to Masjed-Jamei and Koepf in the most general form. The result is then applied to obtain extensions of (i) Knuth's old sum (or the Reed Dawson identity) and (ii) Riordan's identity in the most general form. A few interesting results are obtained as special cases of our main findings.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8ce01ce290b18d999ca1bcb63cafedc1 https://www.ajol.info/index.php/qm/article/view/230231 Zobrazit plný text záznamu