DLMF:7.5.E4 (Q2350): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec

Revision as of 01:38, 2 January 2020

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DLMF:7.5.E4
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    Statements

    Defining formula
    S ⁡ ( z ) = 1 2 - f ⁡ ( z ) ⁢ cos ⁡ ( 1 2 ⁢ π ⁢ z 2 ) - g ⁡ ( z ) ⁢ sin ⁡ ( 1 2 ⁢ π ⁢ z 2 ) . Fresnel-sine-integral 𝑧 1 2 Fresnel-auxilliary-function-f 𝑧 1 2 𝜋 superscript 𝑧 2 Fresnel-auxilliary-function-g 𝑧 1 2 𝜋 superscript 𝑧 2 {\displaystyle{\displaystyle S\left(z\right)=\tfrac{1}{2}-\mathrm{f}\left(z% \right)\cos\left(\tfrac{1}{2}\pi z^{2}\right)-\mathrm{g}\left(z\right)\sin% \left(\tfrac{1}{2}\pi z^{2}\right).}}
    0 references
    DLMF id
    DLMF:7.5.E4
    0 references
    Symbols used
    auxiliary function for Fresnel integrals
    Defining formula
    f ⁡ ( z ) Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E10.m2aadec
    0 references
    auxiliary function for Fresnel integrals
    Defining formula
    g ⁡ ( z ) Fresnel-auxilliary-function-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E11.m2aadec
    0 references
    Fresnel integral
    Defining formula
    S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E8.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
     
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