A Comprehensive Treatment of q-CalculusSundry topics
A Comprehensive Treatment of q-Calculus: Sundry topics
Ernst, Thomas
2012-06-18 00:00:00
[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.]
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A Comprehensive Treatment of q-CalculusSundry 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.]
Published: Jun 18, 2012
Keywords: Bailey Transformation; Summation Formula; Mirror Formula; Great Theoretical Interest; Balanced Series
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