# A Comprehensive Treatment of q-Calculusq-functions of several variables

A Comprehensive Treatment of q-Calculus: q-functions of several variables [We begin with the vector notation for the most important functions and q-Taylor formulas for power series and functions of inverse q-shifted factorials. We continue with a historical introduction to the rest of this long and interesting chapter and to the next chapter as well. We will also define q-Appell functions together with the normal form. Then follows the two definitions of q-Kampé de Fériet functions due to Karlsson and Srivastava. The q-analogue of Appell and Kampé de Fériet’s transformation formulas require the Watson q-shifted factorial in the definition. We continue with Carlitz’ Saalschützian formulas, Andrews’s formal transformations and Carlson’s transformations.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Comprehensive Treatment of q-Calculusq-functions of several variables

68 pages

/lp/springer-journals/a-comprehensive-treatment-of-q-calculus-q-functions-of-several-tzooJU2Enj
Publisher
Springer Basel
ISBN
978-3-0348-0430-1
Pages
359 –426
DOI
10.1007/978-3-0348-0431-8_10
Publisher site
See Chapter on Publisher Site

### Abstract

[We begin with the vector notation for the most important functions and q-Taylor formulas for power series and functions of inverse q-shifted factorials. We continue with a historical introduction to the rest of this long and interesting chapter and to the next chapter as well. We will also define q-Appell functions together with the normal form. Then follows the two definitions of q-Kampé de Fériet functions due to Karlsson and Srivastava. The q-analogue of Appell and Kampé de Fériet’s transformation formulas require the Watson q-shifted factorial in the definition. We continue with Carlitz’ Saalschützian formulas, Andrews’s formal transformations and Carlson’s transformations.]

Published: Jun 18, 2012

Keywords: Reduction Formula; Lauricella Function; Carlitz; Negative Integer Argument; Jackson Formula