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Thomas Ernst
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Thomas Ernst: Uppsala University, Department of Mathematics

Chapter Chapter 8 in A Comprehensive Treatment of q-Calculus, 2012, pp 279-307 from Springer

Abstract: 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.

Keywords: Bailey Transformation; Summation Formula; Mirror Formula; Great Theoretical Interest; Balanced Series (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0431-8_8

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DOI: 10.1007/978-3-0348-0431-8_8

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