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The different tongues of q-calculus
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2008 (English)In: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, Vol. 57, no 2, 81-99 p.Article in journal (Refereed) Published
Abstract [en]

In this review paper we summarize the various dialects of q-calculus: quantum Calculus, time scales, and partitions. The close connection between Gamma q(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.

Place, publisher, year, edition, pages
2008. Vol. 57, no 2, 81-99 p.
Keyword [en]
elliptic functions, theta functions, q-Appell functions, q-addition, Carlitz-AlSalam polynomial
National Category
URN: urn:nbn:se:uu:diva-129896DOI: 10.3176/proc.2008.2.03ISI: 000263771000003OAI: oai:DiVA.org:uu-129896DiVA: diva2:345577
Available from: 2010-08-26 Created: 2010-08-25 Last updated: 2010-08-26Bibliographically approved

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