DLMF:16.12.E2 (Q5247): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11581 / rank
 
Normal rank
Property / Symbols used: Q11581 / qualifier
 
Defining formula:

F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

\genhyperF{2}{1}@{\NVar{a},\NVar{b}}{\NVar{c}}{\NVar{z}}
Property / Symbols used: Q11581 / qualifier
 
xml-id: C16.S2.m5adec

Revision as of 14:40, 2 January 2020

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DLMF:16.12.E2
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    Statements

    Defining formula
    ( F 1 2 ⁡ ( a , b a + b + 1 2 ; z ) ) 2 = F 2 3 ⁡ ( 2 ⁢ a , 2 ⁢ b , a + b a + b + 1 2 , 2 ⁢ a + 2 ⁢ b ; z ) . superscript Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑎 𝑏 1 2 𝑧 2 Gauss-hypergeometric-pFq 3 2 2 𝑎 2 𝑏 𝑎 𝑏 𝑎 𝑏 1 2 2 𝑎 2 𝑏 𝑧 {\displaystyle{\displaystyle\left({{}_{2}F_{1}}\left({a,b\atop a+b+\frac{1}{2}% };z\right)\right)^{2}={{}_{3}F_{2}}\left({2a,2b,a+b\atop a+b+\frac{1}{2},2a+2b% };z\right).}}
    0 references
    DLMF id
    DLMF:16.12.E2
    0 references
    Symbols used
    Q11581
    Defining formula
    F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}
    xml-id
    C16.S2.m5adec
    0 references
     
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