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Sundry topics

In: A Comprehensive Treatment of q-Calculus

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  • Thomas Ernst

    (Uppsala University, Department of Mathematics)

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.

Suggested Citation

  • Thomas Ernst, 2012. "Sundry topics," Springer Books, in: A Comprehensive Treatment of q-Calculus, edition 127, chapter 0, pages 279-307, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0431-8_8
    DOI: 10.1007/978-3-0348-0431-8_8
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