DLMF:15.4.E2 (Q4985): 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.m2aadec

Revision as of 12:47, 2 January 2020

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DLMF:15.4.E2
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    Statements

    test
    F ⁡ ( 1 2 , 1 ; 3 2 ; z 2 ) = 1 2 ⁢ z ⁢ ln ⁡ ( 1 + z 1 - z ) , Gauss-hypergeometric-F 1 2 1 3 2 superscript 𝑧 2 1 2 𝑧 1 𝑧 1 𝑧 {\displaystyle{\displaystyle F\left(\tfrac{1}{2},1;\tfrac{3}{2};z^{2}\right)=% \frac{1}{2z}\ln\left(\frac{1+z}{1-z}\right),}}
    0 references
    DLMF id
    DLMF:15.4.E2
    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.m2aadec
    0 references
     
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