DLMF:16.6.E1 (Q5216): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11125 / rank
 
Normal rank
Property / Symbols used: Q11125 / qualifier
 
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)}}

\genhyperF{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{z}}
Property / Symbols used: Q11125 / qualifier
 
xml-id: C16.S2.m1adec

Revision as of 14:34, 2 January 2020

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DLMF:16.6.E1
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    Statements

    Defining formula
    F 2 3 ⁡ ( a , b , c a - b + 1 , a - c + 1 ; z ) = ( 1 - z ) - a ⁢ F 2 3 ⁡ ( a - b - c + 1 , 1 2 ⁢ a , 1 2 ⁢ ( a + 1 ) a - b + 1 , a - c + 1 ; - 4 ⁢ z ( 1 - z ) 2 ) . Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑎 𝑏 1 𝑎 𝑐 1 𝑧 superscript 1 𝑧 𝑎 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 1 1 2 𝑎 1 2 𝑎 1 𝑎 𝑏 1 𝑎 𝑐 1 4 𝑧 superscript 1 𝑧 2 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,b,c\atop a-b+1,a-c+1};z% \right)=(1-z)^{-a}{{}_{3}F_{2}}\left({a-b-c+1,\frac{1}{2}a,\frac{1}{2}(a+1)% \atop a-b+1,a-c+1};\frac{-4z}{(1-z)^{2}}\right).}}
    0 references
    DLMF id
    DLMF:16.6.E1
    0 references
    Symbols used
    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.m1adec
    0 references
     
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