DLMF:16.4.E12 (Q5206): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11697 / rank
 
Normal rank
Property / Symbols used: Q11697 / qualifier
 
Defining formula:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11697 / qualifier
 
xml-id: C16.S4.XMD3.m1adec

Revision as of 14:32, 2 January 2020

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DLMF:16.4.E12
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    Statements

    Defining formula
    ( a - d ) ⁢ ( b - d ) ⁢ ( c - d ) ⁢ ( F 2 3 ⁡ ( a , b , c d + 1 , e ; 1 ) - F 2 3 ⁡ ( a , b , c d , e ; 1 ) ) + a ⁢ b ⁢ c ⁢ F 2 3 ⁡ ( a , b , c d , e ; 1 ) = d ⁢ ( d - 1 ) ⁢ ( a + b + c - d - e + 1 ) ⁢ ( F 2 3 ⁡ ( a , b , c d , e ; 1 ) - F 2 3 ⁡ ( a , b , c d - 1 , e ; 1 ) ) , 𝑎 𝑑 𝑏 𝑑 𝑐 𝑑 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 1 𝑒 1 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 𝑒 1 𝑎 𝑏 𝑐 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 𝑒 1 𝑑 𝑑 1 𝑎 𝑏 𝑐 𝑑 𝑒 1 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 𝑒 1 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 1 𝑒 1 {\displaystyle{\displaystyle(a-d)(b-d)(c-d)\left({{}_{3}F_{2}}\left({a,b,c% \atop d+1,e};1\right)-{{}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)\right)+abc{% {}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)=d(d-1)(a+b+c-d-e+1)\left({{}_{3}F_% {2}}\left({a,b,c\atop d,e};1\right)-{{}_{3}F_{2}}\left({a,b,c\atop d-1,e};1% \right)\right),}}
    0 references
    DLMF id
    DLMF:16.4.E12
    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.m1aidec
    0 references
    Q11695
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C16.S4.XMD1.m1adec
    0 references
    Q11696
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C16.S4.XMD2.m1adec
    0 references
    Q11697
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C16.S4.XMD3.m1adec
    0 references
     
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