DLMF:15.4.E28 (Q5012): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / rank
 
Normal rank
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
 
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)}}

\hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
 
xml-id: C15.S2.E1.m2azdec

Revision as of 13:50, 2 January 2020

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DLMF:15.4.E28
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    Statements

    Defining formula
    F ⁡ ( a , b ; 1 2 ⁢ a + 1 2 ⁢ b + 1 2 ; 1 2 ) = π ⁢ Γ ⁡ ( 1 2 ⁢ a + 1 2 ⁢ b + 1 2 ) Γ ⁡ ( 1 2 ⁢ a + 1 2 ) ⁢ Γ ⁡ ( 1 2 ⁢ b + 1 2 ) . Gauss-hypergeometric-F 𝑎 𝑏 1 2 𝑎 1 2 𝑏 1 2 1 2 𝜋 Euler-Gamma 1 2 𝑎 1 2 𝑏 1 2 Euler-Gamma 1 2 𝑎 1 2 Euler-Gamma 1 2 𝑏 1 2 {\displaystyle{\displaystyle F\left(a,b;\tfrac{1}{2}a+\tfrac{1}{2}b+\tfrac{1}{% 2};\tfrac{1}{2}\right)=\sqrt{\pi}\frac{\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}b% +\tfrac{1}{2}\right)}{\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}\right)\Gamma\left% (\tfrac{1}{2}b+\tfrac{1}{2}\right)}.}}
    0 references
    DLMF id
    DLMF:15.4.E28
    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.m2afdec
    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.m2azdec
    0 references
     
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