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DLMF:7.11.E7 - MaRDI portal

DLMF:7.11.E7 (Q3107)

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DLMF:7.11.E7
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    Statements

    DLMF defining formula
    C ⁡ ( z ) = z ⁢ F 2 1 ⁡ ( 1 4 ; 5 4 , 1 2 ; - 1 16 ⁢ π 2 ⁢ z 4 ) , Fresnel-cosine-integral 𝑧 𝑧 Gauss-hypergeometric-pFq 1 2 1 4 5 4 1 2 1 16 superscript 𝜋 2 superscript 𝑧 4 {\displaystyle{\displaystyle C\left(z\right)=z{{}_{1}F_{2}}\left(\tfrac{1}{4};% \tfrac{5}{4},\tfrac{1}{2};-\tfrac{1}{16}\pi^{2}z^{4}\right),}}
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    Symbols used
    Fresnel integral
    DLMF defining formula
    C ⁡ ( z ) Fresnel-cosine-integral 𝑧 {\displaystyle{\displaystyle C\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E7.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.m1adec
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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.m2afdec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1fdec
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    Identifiers

     
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