The different tongues of q-calculus

Proceedings of the Estonian Academy of Sciences

Thomas Ernst¹ 

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关键词: elliptic functions;    theta functions;    q-Appell functions;    q-addition;    Carlitz–AlSalam polynomial;   

DOI  :  10.3176/proc.2008.2.03

学科分类：化学（综合）

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

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.

【 授权许可】

Unknown