DLMF:7.5.E6 (Q2352): 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.m2acdec

Revision as of 01:39, 2 January 2020

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DLMF:7.5.E6
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    Statements

    e ± 1 2 π i z 2 ( g ( z ) ± i f ( z ) ) = 1 2 ( 1 ± i ) - ( C ( z ) ± i S ( z ) ) . superscript 𝑒 plus-or-minus 1 2 𝜋 𝑖 superscript 𝑧 2 plus-or-minus Fresnel-auxilliary-function-g 𝑧 𝑖 Fresnel-auxilliary-function-f 𝑧 1 2 plus-or-minus 1 𝑖 plus-or-minus Fresnel-cosine-integral 𝑧 𝑖 Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle e^{\pm\frac{1}{2}\pi iz^{2}}(\mathrm{g}\left(z% \right)\pm i\mathrm{f}\left(z\right))=\tfrac{1}{2}(1\pm i)-(C\left(z\right)\pm iS% \left(z\right)).}}
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    DLMF:7.5.E6
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    f ( z ) Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    C7.S2.E10.m2acdec
    0 references