DLMF:15.16.E1 (Q5178): 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.m2adec

Revision as of 14:26, 2 January 2020

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DLMF:15.16.E1
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    Statements

    test
    F ⁡ ( a , b c - 1 2 ; z ) ⁢ F ⁡ ( c - a , c - b c + 1 2 ; z ) = ∑ s = 0 ∞ ( c ) s ( c + 1 2 ) s ⁢ A s ⁢ z s , Gauss-hypergeometric-F 𝑎 𝑏 𝑐 1 2 𝑧 Gauss-hypergeometric-F 𝑐 𝑎 𝑐 𝑏 𝑐 1 2 𝑧 superscript subscript 𝑠 0 Pochhammer 𝑐 𝑠 Pochhammer 𝑐 1 2 𝑠 subscript 𝐴 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle F\left({a,b\atop c-\frac{1}{2}};z\right)F\left({c% -a,c-b\atop c+\frac{1}{2}};z\right)=\sum_{s=0}^{\infty}\frac{{\left(c\right)_{% s}}}{{\left(c+\frac{1}{2}\right)_{s}}}A_{s}z^{s},}}
    0 references
    DLMF id
    DLMF:15.16.E1
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    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.m2adec
    0 references
     
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