DLMF:16.12.E2 (Q5247)

From DRMF
Revision as of 14:40, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:16.12.E2
No description defined

    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
    Q11125
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1aadec
    0 references
    Q11692
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1adec
    0 references
    Q11693
    Defining formula
    a , a 1 , … , a p 𝑎 subscript 𝑎 1 … subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
    xml-id
    C16.S1.XMD4.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5247&oldid=49619"