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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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The different tongues of q-calculus; pp. 81–99

(Full article in PDF format) doi: 10.3176/proc.2008.2.03


Authors

Thomas Ernst

Abstract

In this review paper we summarize the various dialects of q-calculus: quantum calculus, time scales, and partitions. The close connection between Γq(x) functions on the one hand, and elliptic functions and theta functions on the other hand will be shown. The advantages of the Heine notation will be illustrated by the (q-)Euler reflection formula, q-Appell functions, Carlitz–AlSalam polynomials, and the so-called q-addition. We conclude with some short biographies about famous scientists in q-calculus.

Keywords

elliptic functions, theta functions, q-Appell functions, q-addition, Carlitz–AlSalam polynomial.

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Current Issue: Vol. 68, Issue 3, 2019




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