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DLMF:7.11.E8 - MaRDI portal

DLMF:7.11.E8 (Q3108)

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DLMF:7.11.E8
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    Statements

    DLMF defining formula
    S ⁡ ( z ) = 1 6 ⁢ π ⁢ z 3 ⁢ F 2 1 ⁡ ( 3 4 ; 7 4 , 3 2 ; - 1 16 ⁢ π 2 ⁢ z 4 ) . Fresnel-sine-integral 𝑧 1 6 𝜋 superscript 𝑧 3 Gauss-hypergeometric-pFq 1 2 3 4 7 4 3 2 1 16 superscript 𝜋 2 superscript 𝑧 4 {\displaystyle{\displaystyle S\left(z\right)=\tfrac{1}{6}\pi z^{3}{{}_{1}F_{2}% }\left(\tfrac{3}{4};\tfrac{7}{4},\tfrac{3}{2};-\tfrac{1}{16}\pi^{2}z^{4}\right% ).}}
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    Symbols used
    Fresnel integral
    DLMF defining formula
    S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E8.m2aadec
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    alternatively F q p ( a ; b ; z ) or F q p ( a b ; z ) generalized hypergeometric function
    DLMF defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1aadec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1gdec
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    Identifiers

     
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