DLMF:17.2.E48 (Q5338)

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Language	Label	Description	Also known as
English	DLMF:17.2.E48	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}f(x){\mathrm{d}}_{q}x=\lim_{n\to% \infty}\int_{0}^{q^{-n}}f(x){\mathrm{d}}_{q}x=(1-q)\sum_{j=-\infty}^{\infty}f(% q^{j})q^{j},}}

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DLMF:17.2.E48

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3acdec

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Defining formula

{\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}

C17.S2.SS5.p1.m3acdec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1atdec

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Defining formula

{\displaystyle{\displaystyle j}}

C17.S1.XMD2.m1mdec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1amdec

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Defining formula

{\displaystyle{\displaystyle x}}

C17.S1.XMD8.m1cdec

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