q-Hypergeometric Functions

Daniel Duverney

Chapter Chapter 10 in An Introduction to Hypergeometric Functions, 2024, pp 317-344 from Springer

Abstract: Abstract Throughout this chapter, q ∈ 0 , 1 $$q\in \left ] 0,1\right [ $$ is a real number. We present here a short introduction to q-hypergeometric functions, which yield the usual hypergeometric functions as a limit case when q → 1. $$ q\rightarrow 1.$$ Hence, we define, in Sect. 10.1, q-analogues of Pochhammer’s symbol, binomial coefficients, differentiation and integration, and exponential and logarithm functions. In Sect. 10.2, we introduce the most general q-hypergeometric functions and study in some detail the q-analogues of the binomial function and of the Gauss hypergeometric function. Finally, Sect. 10.3 is devoted to the proof of some summation formulas.

Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-65144-1_10

Ordering information: This item can be ordered from
http://www.springer.com/9783031651441

DOI: 10.1007/978-3-031-65144-1_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().