DLMF:15.8.E33 (Q5090): Difference between revisions

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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.m2avdec
Property / Symbols used
 
Property / Symbols used: Q11644 / rank
 
Normal rank
Property / Symbols used: Q11644 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11644 / qualifier
 
xml-id: C15.S1.XMD3.m1afdec

Latest revision as of 13:07, 2 January 2020

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DLMF:15.8.E33
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    Statements

    test
    F ⁡ ( 1 3 , 2 3 1 ; 1 - ( 1 - z 1 + 2 ⁢ z ) 3 ) = ( 1 + 2 ⁢ z ) ⁢ F ⁡ ( 1 3 , 2 3 1 ; z 3 ) , Gauss-hypergeometric-F 1 3 2 3 1 1 superscript 1 𝑧 1 2 𝑧 3 1 2 𝑧 Gauss-hypergeometric-F 1 3 2 3 1 superscript 𝑧 3 {\displaystyle{\displaystyle F\left({\frac{1}{3},\frac{2}{3}\atop 1};1-\left(% \frac{1-z}{1+2z}\right)^{3}\right)=(1+2z)F\left({\frac{1}{3},\frac{2}{3}\atop 1% };z^{3}\right),}}
    0 references
    DLMF id
    DLMF:15.8.E33
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ 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.m2avdec
    0 references
    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1afdec
    0 references
     
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