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Title:
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Authors:
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Publisher Information:
Taylor \& Francis, Abingdon, Oxfordshire
Subject Terms:
Basic hypergeometric functions in one variable, \({}_r\phi_s\), Other basic hypergeometric functions and integrals in several variables, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
Document Type:
Academic journal Article
File Description:
application/xml
DOI:
10.1080/10652469308819019
Access URL:
https://zbmath.org/768926
Accession Number:
edsair.c2b0b933574d..e1795e56da8c5368d5d0f47ab0c0a599
Database:
OpenAIRE

Further Information

The author here studies a common generalization of both the Jackson and the Hahn-Exton \(q\)-Bessel function. For this \(q\)-analogue of the Bessel function an analogue of Graf's addition formula is proved. From this result he obtains Hansen-Lommel type orthogonality relations and a \(q\)- analogue of Lommel's formula. These results yield \(q\)-analogues of an integral of Weber and Sonine and of the Hankel (or Fourier-Bessel) transform.