Formula:3082

Digital Library of Mathematical Functions ID 7.7.E14

${\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\frac{(2\pi)^{-3/2}}{2\pi i}\int_{c-i\infty}^{c+i\infty}\zeta^{-s}\Gamma\left(s\right)\Gamma\left(s+\tfrac{1}{2}\right)\*\Gamma\left(s+\tfrac{1}{4}\right)\Gamma\left(\tfrac{3}{4}-s\right)\mathrm{d}s.}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}$: auxiliary function for Fresnel integrals
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\zeta}}$: change of variable
• ${\displaystyle{\displaystyle c}}$: constant
 

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