DLMF:15.4.E30 (Q5014): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11645 / rank
 
Normal rank
Property / Symbols used: Q11645 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11645 / qualifier
 
xml-id: C15.S1.XMD4.m1wdec

Revision as of 13:51, 2 January 2020

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DLMF:15.4.E30
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    Statements

    Defining formula
    F ⁡ ( a , 1 - a ; b ; 1 2 ) = 2 1 - b ⁢ π ⁢ Γ ⁡ ( b ) Γ ⁡ ( 1 2 ⁢ a + 1 2 ⁢ b ) ⁢ Γ ⁡ ( 1 2 ⁢ b - 1 2 ⁢ a + 1 2 ) . Gauss-hypergeometric-F 𝑎 1 𝑎 𝑏 1 2 superscript 2 1 𝑏 𝜋 Euler-Gamma 𝑏 Euler-Gamma 1 2 𝑎 1 2 𝑏 Euler-Gamma 1 2 𝑏 1 2 𝑎 1 2 {\displaystyle{\displaystyle F\left(a,1-a;b;\tfrac{1}{2}\right)=\frac{2^{1-b}% \sqrt{\pi}\Gamma\left(b\right)}{\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}b\right)% \Gamma\left(\tfrac{1}{2}b-\tfrac{1}{2}a+\tfrac{1}{2}\right)}.}}
    0 references
    DLMF id
    DLMF:15.4.E30
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ahdec
    0 references
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    Defining formula
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2aabdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1wdec
    0 references
     
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