Formula:499

Digital Library of Mathematical Functions ID 1.14.E38

${\displaystyle{\displaystyle\int^{\infty}_{0}(f(x))^{2}\mathrm{d}x=\frac{1}{2\pi}\int^{\infty}_{-\infty}{\left|\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(\tfrac{1}{2}+it\right)\right|^{2}}\mathrm{d}t.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Mellin transform
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
 

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