Formula:3064

Digital Library of Mathematical Functions ID 7.6.E7

${\displaystyle{\displaystyle S\left(z\right)=-\cos\left(\tfrac{1}{2}\pi z^{2}\right)\sum_{n=0}^{\infty}\frac{(-1)^{n}\pi^{2n+1}}{1\cdot 3\cdots(4n+3)}z^{4n+3}+\sin\left(\tfrac{1}{2}\pi z^{2}\right)\sum_{n=0}^{\infty}\frac{(-1)^{n}\pi^{2n}}{1\cdot 3\cdots(4n+1)}z^{4n+1}.}}$

Symbols List

• ${\displaystyle{\displaystyle S\left(\NVar{z}\right)}}$: Fresnel integral
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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