DLMF:7.7.E12 (Q2382): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: auxiliary function for Fresnel integrals / rank
 
Normal rank
Property / Symbols used: auxiliary function for Fresnel integrals / qualifier
 
Defining formula:

f ( z ) Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}

\auxFresnelf@{\NVar{z}}
Property / Symbols used: auxiliary function for Fresnel integrals / qualifier
 
xml-id: C7.S2.E10.m2aadec

Revision as of 01:45, 2 January 2020

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DLMF:7.7.E12
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    Statements

    g ( z ) + i f ( z ) = e - π i z 2 / 2 z e π i t 2 / 2 d t . Fresnel-auxilliary-function-g 𝑧 𝑖 Fresnel-auxilliary-function-f 𝑧 superscript 𝑒 𝜋 𝑖 superscript 𝑧 2 2 superscript subscript 𝑧 superscript 𝑒 𝜋 𝑖 superscript 𝑡 2 2 𝑡 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)+i\mathrm{f}\left(z\right)% =e^{-\pi iz^{2}/2}\int_{z}^{\infty}e^{\pi it^{2}/2}\mathrm{d}t.}}
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    DLMF:7.7.E12
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    f ( z ) Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    C7.S2.E10.m2aadec
    0 references