Formula:6035

Digital Library of Mathematical Functions ID 17.2.E48

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

Symbols List

• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}$:
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle j}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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