DLMF:7.2.E11 (Q2333): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Fresnel integral / rank
 
Normal rank
Property / Symbols used: Fresnel integral / qualifier
 
Defining formula:

S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}

\Fresnelsinint@{\NVar{z}}
Property / Symbols used: Fresnel integral / qualifier
 
xml-id: C7.S2.E8.m2acdec

Revision as of 01:37, 2 January 2020

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DLMF:7.2.E11
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    Statements

    Defining formula
    g ⁡ ( z ) = ( 1 2 - C ⁡ ( z ) ) ⁢ cos ⁡ ( 1 2 ⁢ π ⁢ z 2 ) + ( 1 2 - S ⁡ ( z ) ) ⁢ sin ⁡ ( 1 2 ⁢ π ⁢ z 2 ) . Fresnel-auxilliary-function-g 𝑧 1 2 Fresnel-cosine-integral 𝑧 1 2 𝜋 superscript 𝑧 2 1 2 Fresnel-sine-integral 𝑧 1 2 𝜋 superscript 𝑧 2 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\left(\tfrac{1}{2}-C\left% (z\right)\right)\cos\left(\tfrac{1}{2}\pi z^{2}\right)+\left(\tfrac{1}{2}-S% \left(z\right)\right)\sin\left(\tfrac{1}{2}\pi z^{2}\right).}}
    0 references
    DLMF id
    DLMF:7.2.E11
    0 references
    Symbols used
    Fresnel integral
    Defining formula
    C ⁡ ( z ) Fresnel-cosine-integral 𝑧 {\displaystyle{\displaystyle C\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E7.m2acdec
    0 references
    Fresnel integral
    Defining formula
    S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E8.m2acdec
    0 references
     
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