Work

Expansions of averaged truncations of basic hypergeometric series

Year: 2024

Type: article

Abstract: Motivated by recent work of George Andrews and Mircea Merca [J. Combin. Theory Ser. A 119 (2012), pp. 1639–1643] on the expansion of the quotient of the truncation of Euler’s pentagonal number series by the complete series, we provide similar expansion results for averages involving truncations of selected, more general, basic hypergeometric series. In particular, our expansions include new results for averaged truncations of the series appearing in the Jacobi triple product identity, the q q -Gauß summation, and the very-well-poised 5 ϕ 5 {}_5\phi _5 summation. We show how special cases of our expansions can be used to recover various existing results. In addition, we establish new inequalities, such as one for a refinement of the number of partitions into three different colors.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/16775

Authors: Michael Schlosser, Nian Hong Zhou

Institution: University of Vienna

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Austrian Science Fund

Awards: Elliptic hypergeometric combinatorics, G9000027448