DLMF:15.6.E8 (Q5046): 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
 
test:

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.m2agdec

Revision as of 12:58, 2 January 2020

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DLMF:15.6.E8
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    Statements

    test
    𝐅 ⁡ ( a , b ; c ; z ) = 1 Γ ⁡ ( c - d ) ⁢ ∫ 0 1 𝐅 ⁡ ( a , b ; d ; z ⁢ t ) ⁢ t d - 1 ⁢ ( 1 - t ) c - d - 1 ⁢ d t , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 1 Euler-Gamma 𝑐 𝑑 superscript subscript 0 1 scaled-hypergeometric-bold-F 𝑎 𝑏 𝑑 𝑧 𝑡 superscript 𝑡 𝑑 1 superscript 1 𝑡 𝑐 𝑑 1 𝑡 {\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=\frac{1}{\Gamma% \left(c-d\right)}\int_{0}^{1}\mathbf{F}\left(a,b;d;zt\right)t^{d-1}(1-t)^{c-d-% 1}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:15.6.E8
    0 references
    constraint
    | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
    0 references
    ℜ ⁡ c > ℜ ⁡ d > 0 𝑐 𝑑 0 {\displaystyle{\displaystyle\Re c>\Re d>0}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
    0 references
     
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