\(q\)-extension of the Euler formula and trigonometric functions
type: Item
instance of: scholarly article
title: \(q\)-extension of the Euler formula and trigonometric functions
zbMATH Open document ID: 1188.33001
DOI: 10.1134/S1061920807030041
author: Taekyun Kim
published in: Russian Journal of Mathematical Physics
publication date: 2009-11-10T00:00:00Z
review text: Replacing the factorial \(n!\) by the \(q\)-factorial \[ [n]_q!=\prod_{k=1}^n\frac{1-q^k}{1-q} \] the author defines the \(q\)-exponential function \[ e_q(z)=\sum_{n=0}^\infty\frac{z^n}{[n]_q!} \] and the related \(q\)-trigonometric functions \(\cos_q(z)\) and \(\sin_q(z)\) as the real and imaginary parts of \(e_q(iz)\). Then he derives \(q\)-analogues of classical formulae satisfied by these functions.
reviewed by: Wadim Zudilin
Mathematics Subject Classification ID: 33B10
Mathematics Subject Classification ID: 33D15
zbMATH DE Number: 5627977
zbMATH Keywords: exponential function
zbMATH Keywords: trigonometric function
zbMATH Keywords: \(q\)-analogue
Wikidata QID: Q56502273
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5627977