Result: On a calculus for the \(T_{k,q, x}\)-operator

Title:
On a calculus for the \(T_{k,q, x}\)-operator
Authors:
Khan, Mumtaz Ahmad
Publisher Information:
Bulgarian Academy of Sciences, National Committee for Mathematics, Sofia
Subject Terms:
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Fractional derivatives and integrals, Basic hypergeometric integrals and functions defined by them
Document Type:
Academic journal Article
File Description:
application/xml
Access URL:
https://zbmath.org/816219
Accession Number:
edsair.c2b0b933574d..46e672a9465f9030730f9398ca1e322d
Database:
OpenAIRE

Further Information

The present paper deals with the calculus of \(T_{k,q,x}\)-operator. The operator, which is a \(q\)-extension of the operators given earlier by \textit{W. A. Al-Salam} [Duke Math. J. 31, 127-142 (1964; Zbl 0124.03402)]\ and \textit{H. B. Mittal} [Glasnik Mat., III. Ser. 6(26), 45-53 (1971; Zbl 0247.33010)]\ has been used in another author's communication to obtain operational representations for various \(q\)-polynomials which are very useful in finding the generating functions and the recurrence relations of the \(q\)-polynomials.