DLMF:7.11.E7 (Q2409): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
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.m2afdec

Revision as of 01:49, 2 January 2020

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DLMF:7.11.E7
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    Statements

    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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    DLMF:7.11.E7
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    C ( z ) Fresnel-cosine-integral 𝑧 {\displaystyle{\displaystyle C\left(\NVar{z}\right)}}
    C7.S2.E7.m2aadec
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    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)}}
    C16.S2.m1adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2afdec
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