DLMF:15.8.E18 (Q5075)

From testwiki
Revision as of 13:04, 2 January 2020 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:15.8.E18
No description defined

    Statements

    test
    F ⁡ ( a , b 1 2 ⁢ ( a + b + 1 ) ; z ) = F ⁡ ( 1 2 ⁢ a , 1 2 ⁢ b 1 2 ⁢ ( a + b + 1 ) ; 4 ⁢ z ⁢ ( 1 - z ) ) , Gauss-hypergeometric-F 𝑎 𝑏 1 2 𝑎 𝑏 1 𝑧 Gauss-hypergeometric-F 1 2 𝑎 1 2 𝑏 1 2 𝑎 𝑏 1 4 𝑧 1 𝑧 {\displaystyle{\displaystyle F\left({a,b\atop\frac{1}{2}(a+b+1)};z\right)=F% \left({\frac{1}{2}a,\frac{1}{2}b\atop\frac{1}{2}(a+b+1)};4z(1-z)\right),}}
    0 references
    DLMF id
    DLMF:15.8.E18
    0 references
    constraint
    ℜ ⁡ z < 1 2 𝑧 1 2 {\displaystyle{\displaystyle\Re z<\frac{1}{2}}}
    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.m2agdec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q5075&oldid=28975"