DLMF:19.19.E7 (Q6367): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11861 / rank
 
Normal rank
Property / Symbols used: Q11861 / qualifier
 
Defining formula:

𝐙 𝐙 {\displaystyle{\displaystyle\mathbf{Z}}}

\mathbf{Z}
Property / Symbols used: Q11861 / qualifier
 
xml-id: C19.S19.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q11862 / rank
 
Normal rank
Property / Symbols used: Q11862 / qualifier
 
Defining formula:

A 𝐴 {\displaystyle{\displaystyle A}}

A
Property / Symbols used: Q11862 / qualifier
 
xml-id: C19.S19.XMD7.m1dec

Latest revision as of 13:56, 2 January 2020

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DLMF:19.19.E7
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    Statements

    Defining formula
    R - a ⁡ ( 𝟏 𝟐 ; 𝐳 ) = A - a ⁢ ∑ N = 0 ∞ ( a ) N ( 1 2 ⁢ n ) N ⁢ T N ⁢ ( 𝟏 𝟐 , 𝐙 ) , Carlson-integral-R 𝑎 1 2 𝐳 superscript 𝐴 𝑎 superscript subscript 𝑁 0 Pochhammer 𝑎 𝑁 Pochhammer 1 2 𝑛 𝑁 subscript 𝑇 𝑁 1 2 𝐙 {\displaystyle{\displaystyle R_{-a}\left(\boldsymbol{{\tfrac{1}{2}}};\mathbf{z% }\right)=A^{-a}\sum_{N=0}^{\infty}\frac{{\left(a\right)_{N}}}{{\left(\tfrac{1}% {2}n\right)_{N}}}T_{N}(\boldsymbol{{\tfrac{1}{2}}},\mathbf{Z}),}}
    0 references
    DLMF id
    DLMF:19.19.E7
    0 references
    Symbols used
    multivariate hypergeometric function
    Defining formula
    R - a ⁡ ( b 1 , … , b n ; z 1 , … , z n ) Carlson-integral-R 𝑎 subscript 𝑏 1 … subscript 𝑏 𝑛 subscript 𝑧 1 … subscript 𝑧 𝑛 {\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}
    xml-id
    C19.S16.E9.m2acdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1addec
    0 references
    Q11820
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C19.S1.XMD3.m1edec
    0 references
    Q11858
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C19.S19.XMD1.m1ddec
    0 references
    Q11859
    Defining formula
    T N ⁢ ( 𝐛 , 𝐳 ) subscript 𝑇 𝑁 𝐛 𝐳 {\displaystyle{\displaystyle T_{N}(\mathbf{b},\mathbf{z})}}
    xml-id
    C19.S19.XMD2.m1ddec
    0 references
    Q11861
    Defining formula
    𝐙 𝐙 {\displaystyle{\displaystyle\mathbf{Z}}}
    xml-id
    C19.S19.XMD5.m1dec
    0 references
    Q11862
    Defining formula
    A 𝐴 {\displaystyle{\displaystyle A}}
    xml-id
    C19.S19.XMD7.m1dec
    0 references
     
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