DLMF:19.19.E5 (Q6365): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
Defining formula:

( 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.m1acdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec
Property / Symbols used
 
Property / Symbols used: Q11818 / rank
 
Normal rank
Property / Symbols used: Q11818 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11818 / qualifier
 
xml-id: C19.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11820 / rank
 
Normal rank
Property / Symbols used: Q11820 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11820 / qualifier
 
xml-id: C19.S1.XMD3.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11858 / rank
 
Normal rank
Property / Symbols used: Q11858 / qualifier
 
Defining formula:

N 𝑁 {\displaystyle{\displaystyle N}}

N
Property / Symbols used: Q11858 / qualifier
 
xml-id: C19.S19.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11859 / rank
 
Normal rank
Property / Symbols used: Q11859 / qualifier
 
Defining formula:

T N ⁢ ( 𝐛 , 𝐳 ) subscript 𝑇 𝑁 𝐛 𝐳 {\displaystyle{\displaystyle T_{N}(\mathbf{b},\mathbf{z})}}

T_{N}(\mathbf{b},\mathbf{z})
Property / Symbols used: Q11859 / qualifier
 
xml-id: C19.S19.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: symmetric function (locally) / rank
 
Normal rank
Property / Symbols used: symmetric function (locally) / qualifier
 
Defining formula:

E s ⁢ ( 𝐳 ) subscript 𝐸 𝑠 𝐳 {\displaystyle{\displaystyle E_{s}(\mathbf{z})}}

E_{s}(\mathbf{z})
Property / Symbols used: symmetric function (locally) / qualifier
 
xml-id: C19.S19.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11860 / rank
 
Normal rank
Property / Symbols used: Q11860 / qualifier
 
Defining formula:

M 𝑀 {\displaystyle{\displaystyle M}}

M
Property / Symbols used: Q11860 / qualifier
 
xml-id: C19.S19.XMD4.m1dec

Latest revision as of 13:56, 2 January 2020

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English
DLMF:19.19.E5
No description defined

    Statements

    Defining formula
    T N ⁢ ( 𝟏 𝟐 , 𝐳 ) = ∑ ( - 1 ) M + N ⁢ ( 1 2 ) M ⁢ E 1 m 1 ⁢ ( 𝐳 ) ⁢ ⋯ ⁢ E n m n ⁢ ( 𝐳 ) m 1 ! ⁢ ⋯ ⁢ m n ! , subscript 𝑇 𝑁 1 2 𝐳 superscript 1 𝑀 𝑁 Pochhammer 1 2 𝑀 superscript subscript 𝐸 1 subscript 𝑚 1 𝐳 ⋯ superscript subscript 𝐸 𝑛 subscript 𝑚 𝑛 𝐳 subscript 𝑚 1 ⋯ subscript 𝑚 𝑛 {\displaystyle{\displaystyle T_{N}(\mathbf{\tfrac{1}{2}},\mathbf{z})=\sum(-1)^% {M+N}{\left(\tfrac{1}{2}\right)_{M}}\frac{E_{1}^{m_{1}}(\mathbf{z})\cdots E_{n% }^{m_{n}}(\mathbf{z})}{m_{1}!\cdots m_{n}!},}}
    0 references
    DLMF id
    DLMF:19.19.E5
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1acdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q11818
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C19.S1.XMD2.m1adec
    0 references
    Q11820
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C19.S1.XMD3.m1ddec
    0 references
    Q11858
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C19.S19.XMD1.m1cdec
    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.m1cdec
    0 references
    symmetric function (locally)
    Defining formula
    E s ⁢ ( 𝐳 ) subscript 𝐸 𝑠 𝐳 {\displaystyle{\displaystyle E_{s}(\mathbf{z})}}
    xml-id
    C19.S19.XMD3.m1adec
    0 references
    Q11860
    Defining formula
    M 𝑀 {\displaystyle{\displaystyle M}}
    xml-id
    C19.S19.XMD4.m1dec
    0 references
     
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