In this review paper we summarize the various dialects of q-calculus: quantum calculus, time scales, and partitions. The close connection between Îq(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, CarlitzâAlSalam polynomials, and the so-called q-addition. We conclude with some short biographies about famous scientists in q-calculus.
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Thomas Ernst (2008) studied this question.