DLMF:15.8.E13 (Q5070): 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.m2abdec

Revision as of 13:03, 2 January 2020

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DLMF:15.8.E13
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    Statements

    test
    F ⁡ ( a , b 2 ⁢ b ; z ) = ( 1 - 1 2 ⁢ z ) - a ⁢ F ⁡ ( 1 2 ⁢ a , 1 2 ⁢ a + 1 2 b + 1 2 ; ( z 2 - z ) 2 ) , Gauss-hypergeometric-F 𝑎 𝑏 2 𝑏 𝑧 superscript 1 1 2 𝑧 𝑎 Gauss-hypergeometric-F 1 2 𝑎 1 2 𝑎 1 2 𝑏 1 2 superscript 𝑧 2 𝑧 2 {\displaystyle{\displaystyle F\left({a,b\atop 2b};z\right)=\left(1-\tfrac{1}{2% }z\right)^{-a}F\left({\tfrac{1}{2}a,\tfrac{1}{2}a+\tfrac{1}{2}\atop b+\tfrac{1% }{2}};\left(\frac{z}{2-z}\right)^{2}\right),}}
    0 references
    DLMF id
    DLMF:15.8.E13
    0 references
    constraint
    | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
    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.m2abdec
    0 references
     
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