DLMF:15.8.E18 (Q5075): Difference between revisions

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Property / constraint
 

ℜ ⁡ z < 1 2 𝑧 1 2 {\displaystyle{\displaystyle\Re z<\frac{1}{2}}}

\realpart@@{z}<\frac{1}{2}
Property / constraint: ℜ ⁡ z < 1 2 𝑧 1 2 {\displaystyle{\displaystyle\Re z<\frac{1}{2}}} / rank
 
Normal rank
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.m2agdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1abdec
Property / Symbols used
 
Property / Symbols used: Q11644 / rank
 
Normal rank
Property / Symbols used: Q11644 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11644 / qualifier
 
xml-id: C15.S1.XMD3.m1qdec
Property / Symbols used
 
Property / Symbols used: Q11645 / rank
 
Normal rank
Property / Symbols used: Q11645 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11645 / qualifier
 
xml-id: C15.S1.XMD4.m1pdec
Property / Symbols used
 
Property / Symbols used: Q11646 / rank
 
Normal rank
Property / Symbols used: Q11646 / qualifier
 
test:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11646 / qualifier
 
xml-id: C15.S1.XMD5.m1pdec

Latest revision as of 13:04, 2 January 2020

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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
    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1qdec
    0 references
    Q11645
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1pdec
    0 references
    Q11646
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1pdec
    0 references
     
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