DLMF:17.3.E5 (Q5345): Difference between revisions

Revision as of 14:53, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:17.3.E5	No description defined

{\displaystyle{\displaystyle\mathrm{cos}_{q}\left(x\right)=\frac{1}{2}(e_{q}% \left(ix\right)+e_{q}\left(-ix\right))=\sum_{n=0}^{\infty}\frac{(1-q)^{2n}(-1)% ^{n}x^{2n}}{\left(q;q\right)_{2n}},}}

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DLMF:17.3.E5

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{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2abdec

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{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

C17.S2.SS1.p1.m2addec

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{\displaystyle{\displaystyle e_{\NVar{q}}\left(\NVar{x}\right)}}

C17.S3.E1.m2abdec

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@@ Property / Symbols used @@
+$$q$$ -exponential function
@@ Property / Symbols used: $$q$$ -exponential function / rank @@
+Normal rank
@@ Property / Symbols used: $$q$$ -exponential function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle e_{\NVar{q}}\left(\NVar{x}\right)}}$ 
\qexp{\NVar{q}}@{\NVar{x}}
@@ Property / Symbols used: $$q$$ -exponential function / qualifier @@
+xml-id: C17.S3.E1.m2abdec