DLMF:15.4.E32 (Q5016): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2ajdec
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
 
test:

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.m2aaddec
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.m2addec
Property / Symbols used
 
Property / Symbols used: Q11645 / rank
 
Normal rank
Property / Symbols used: Q11645 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11645 / qualifier
 
xml-id: C15.S1.XMD4.m1ydec

Latest revision as of 12:51, 2 January 2020

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DLMF:15.4.E32
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    Statements

    test
    F ⁡ ( a , 1 2 + a ; 5 6 + 2 3 ⁢ a ; 1 9 ) = π ⁢ ( 3 4 ) a ⁢ Γ ⁡ ( 5 6 + 2 3 ⁢ a ) Γ ⁡ ( 1 2 + 1 3 ⁢ a ) ⁢ Γ ⁡ ( 5 6 + 1 3 ⁢ a ) . Gauss-hypergeometric-F 𝑎 1 2 𝑎 5 6 2 3 𝑎 1 9 𝜋 superscript 3 4 𝑎 Euler-Gamma 5 6 2 3 𝑎 Euler-Gamma 1 2 1 3 𝑎 Euler-Gamma 5 6 1 3 𝑎 {\displaystyle{\displaystyle F\left(a,\tfrac{1}{2}+a;\tfrac{5}{6}+\tfrac{2}{3}% a;\tfrac{1}{9}\right)=\sqrt{\pi}\left(\frac{3}{4}\right)^{a}\frac{\Gamma\left(% \tfrac{5}{6}+\tfrac{2}{3}a\right)}{\Gamma\left(\tfrac{1}{2}+\tfrac{1}{3}a% \right)\Gamma\left(\tfrac{5}{6}+\tfrac{1}{3}a\right)}.}}
    0 references
    DLMF id
    DLMF:15.4.E32
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ajdec
    0 references
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    test
    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.m2aaddec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q11645
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1ydec
    0 references
     
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