DLMF:15.16.E1 (Q5178): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11648 / rank
 
Normal rank
Property / Symbols used: Q11648 / qualifier
 
test:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q11648 / qualifier
 
xml-id: C15.S1.XMD11.m1dec
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.m1dec
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.m1dec
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q11647 / rank
 
Normal rank
Property / Symbols used: Q11647 / qualifier
 
test:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11647 / qualifier
 
xml-id: C15.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q11689 / rank
 
Normal rank
Property / Symbols used: Q11689 / qualifier
 
test:

A s subscript 𝐴 𝑠 {\displaystyle{\displaystyle A_{s}}}

A_{s}
Property / Symbols used: Q11689 / qualifier
 
xml-id: C15.S16.XMD1.m1dec

Latest revision as of 13:27, 2 January 2020

No description defined
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English
DLMF:15.16.E1
No description defined

    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
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q11648
    test
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C15.S1.XMD11.m1dec
    0 references
    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1dec
    0 references
    Q11645
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1dec
    0 references
    Q11646
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1dec
    0 references
    Q11647
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1dec
    0 references
    Q11689
    test
    A s subscript 𝐴 𝑠 {\displaystyle{\displaystyle A_{s}}}
    xml-id
    C15.S16.XMD1.m1dec
    0 references
     
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