DLMF:7.7.E11 (Q2381)

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No description defined

Language	Label	Description	Also known as
English	DLMF:7.7.E11	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\frac{1}{\pi\sqrt{2}}\int% _{0}^{\infty}\frac{\sqrt{t}e^{-\pi z^{2}t/2}}{t^{2}+1}\mathrm{d}t,}}

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DLMF:7.7.E11

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{\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{1}{4}\pi}}

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auxiliary function for Fresnel integrals

Defining formula

{\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}

C7.S2.E11.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2ajdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1ajdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2ajdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3ajdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{ph}}}

C1.S9.E7.m1addec

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Defining formula

{\displaystyle{\displaystyle z}}

C7.S1.XMD2.m1edec

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