# A Comprehensive Treatment of q-CalculusSundry topics

A Comprehensive Treatment of q-Calculus: Sundry topics [This chapter contains applications of the previous one. Examples are two quadratic q-hypergeometric transformations. Most of the summation formulas are given both in q-hypergeometric form and in q-binomial coefficient form for convenience. We use the q-analogue of Euler’s mirror formula to prove a summation formula. We give another proof of the q-Dixon formula by means of yet another q-analogue of Kummer’s first summation formula. We find a q-analogue of Truesdell’s function and its functional equation. The Bailey transformation for q-series is of great theoretical interest. We find a q-Taylor formula with Lagrange remainder term. Finally, bilateral q-hypergeometric series are treated.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Comprehensive Treatment of q-CalculusSundry topics

29 pages

/lp/springer-journals/a-comprehensive-treatment-of-q-calculus-sundry-topics-GxWMZHvzzy
Publisher
Springer Basel
ISBN
978-3-0348-0430-1
Pages
279 –307
DOI
10.1007/978-3-0348-0431-8_8
Publisher site
See Chapter on Publisher Site

### Abstract

[This chapter contains applications of the previous one. Examples are two quadratic q-hypergeometric transformations. Most of the summation formulas are given both in q-hypergeometric form and in q-binomial coefficient form for convenience. We use the q-analogue of Euler’s mirror formula to prove a summation formula. We give another proof of the q-Dixon formula by means of yet another q-analogue of Kummer’s first summation formula. We find a q-analogue of Truesdell’s function and its functional equation. The Bailey transformation for q-series is of great theoretical interest. We find a q-Taylor formula with Lagrange remainder term. Finally, bilateral q-hypergeometric series are treated.]

Published: Jun 18, 2012

Keywords: Bailey Transformation; Summation Formula; Mirror Formula; Great Theoretical Interest; Balanced Series