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A Comprehensive Treatment of q-CalculusThe different languages of q-calculus

A Comprehensive Treatment of q-Calculus: The different languages of q-calculus [We give a survey of the different schools in q-analysis and introduce difference calculus and Bernoulli numbers to make a preparation for the important fourth chapter. We summarize the different attempts at elliptic and Theta functions, both of which are intimately related to q-calculus. We present the history of trigonometry, prosthaphaeresis, logarithms and calculus, because we claim that Fermat introduced the precursor of the q-integral long before calculus was invented. The Hindenburg combinatoric School gives a background to the discovery of the Schweins q-binomial theorem. The so-called Fakultäten was a forerunner to the Γ function and q-factorial. In the year 1844, Gudermann published his book on elliptic functions and two years later, in 1846, Heine published his important article on q-hypergeometric series, referring to Gauss’s Disquisitiones, pointing out the two q-analogues of the exponential function.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Comprehensive Treatment of q-CalculusThe different languages of q-calculus

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Publisher
Springer Basel
Copyright
© Springer Basel 2012
ISBN
978-3-0348-0430-1
Pages
27 –61
DOI
10.1007/978-3-0348-0431-8_2
Publisher site
See Chapter on Publisher Site

Abstract

[We give a survey of the different schools in q-analysis and introduce difference calculus and Bernoulli numbers to make a preparation for the important fourth chapter. We summarize the different attempts at elliptic and Theta functions, both of which are intimately related to q-calculus. We present the history of trigonometry, prosthaphaeresis, logarithms and calculus, because we claim that Fermat introduced the precursor of the q-integral long before calculus was invented. The Hindenburg combinatoric School gives a background to the discovery of the Schweins q-binomial theorem. The so-called Fakultäten was a forerunner to the Γ function and q-factorial. In the year 1844, Gudermann published his book on elliptic functions and two years later, in 1846, Heine published his important article on q-hypergeometric series, referring to Gauss’s Disquisitiones, pointing out the two q-analogues of the exponential function.]

Published: Jun 18, 2012

Keywords: Hypergeometric Function; Elliptic Function; Theta Function; Formal Power Series; Austrian School

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