1.17.E10

MaRDI QIDQ639

• Label: 1.17.E10

Digital Library of Mathematical Functions ID 1.17.E10

${\displaystyle{\displaystyle\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n)}e^{i(x-a)t}\mathrm{d}t=\sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}}.}}$

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
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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