Formula:9639

Digital Library of Mathematical Functions ID 30.15.E5

${\displaystyle{\displaystyle\int_{-\tau}^{\tau}e^{-\mathrm{i}t\omega}\phi_{n}(t)\mathrm{d}t=(-\mathrm{i})^{n}\sqrt{\frac{2\pi\tau\Lambda_{n}}{\sigma}}\phi_{n}\left(\frac{\tau}{\sigma}\omega\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle n\geq m}}$: integer degree
• ${\displaystyle{\displaystyle\tau>0}}$: parameter
• ${\displaystyle{\displaystyle\sigma>0}}$: parameter
• ${\displaystyle{\displaystyle\phi_{n}(t)}}$: function (locally)
• ${\displaystyle{\displaystyle\Lambda}}$: 30.15.E2
 

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