DLMF:2.7.E6 (Q896): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q11052 / rank
 
Normal rank
Property / Symbols used: Q11052 / qualifier
 
Defining formula:

b s subscript 𝑏 𝑠 {\displaystyle{\displaystyle b_{s}}}

b_{s}
Property / Symbols used: Q11052 / qualifier
 
xml-id: C2.S7.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q11053 / rank
 
Normal rank
Property / Symbols used: Q11053 / qualifier
 
Defining formula:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11053 / qualifier
 
xml-id: C2.S7.XMD11.m1dec
Property / Symbols used
 
Property / Symbols used: Q11049 / rank
 
Normal rank
Property / Symbols used: Q11049 / qualifier
 
Defining formula:

𝐍 𝐍 {\displaystyle{\displaystyle\mathbf{N}}}

\mathbf{N}
Property / Symbols used: Q11049 / qualifier
 
xml-id: C2.S7.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11050 / rank
 
Normal rank
Property / Symbols used: Q11050 / qualifier
 
Defining formula:

w j ⁢ ( z ) subscript 𝑤 𝑗 𝑧 {\displaystyle{\displaystyle w_{j}(z)}}

w_{j}(z)
Property / Symbols used: Q11050 / qualifier
 
xml-id: C2.S7.XMD8.m1adec

Latest revision as of 17:20, 1 January 2020

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DLMF:2.7.E6
No description defined

    Statements

    Defining formula
    w 2 ⁢ ( z ) = ( z - z 0 ) α 2 ⁢ ∑ s = 0 s ≠ α 1 - α 2 ∞ b s ⁢ ( z - z 0 ) s + c ⁢ w 1 ⁢ ( z ) ⁢ ln ⁡ ( z - z 0 ) , subscript 𝑤 2 𝑧 superscript 𝑧 subscript 𝑧 0 subscript 𝛼 2 superscript subscript 𝑠 0 𝑠 subscript 𝛼 1 subscript 𝛼 2 subscript 𝑏 𝑠 superscript 𝑧 subscript 𝑧 0 𝑠 𝑐 subscript 𝑤 1 𝑧 𝑧 subscript 𝑧 0 {\displaystyle{\displaystyle w_{2}(z)=(z-z_{0})^{\alpha_{2}}\sum_{% \begin{subarray}{c}s=0\\ s\neq\alpha_{1}-\alpha_{2}\end{subarray}}^{\infty}b_{s}(z-z_{0})^{s}+cw_{1}(z)% \ln\left(z-z_{0}\right),}}
    0 references
    DLMF id
    DLMF:2.7.E6
    0 references
    constraint
    z ∈ 𝐍 𝑧 𝐍 {\displaystyle{\displaystyle z\in\mathbf{N}}}
    0 references
    Symbols used
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q11052
    Defining formula
    b s subscript 𝑏 𝑠 {\displaystyle{\displaystyle b_{s}}}
    xml-id
    C2.S7.XMD10.m1dec
    0 references
    Q11053
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C2.S7.XMD11.m1dec
    0 references
    Q11049
    Defining formula
    𝐍 𝐍 {\displaystyle{\displaystyle\mathbf{N}}}
    xml-id
    C2.S7.XMD4.m1adec
    0 references
    Q11050
    Defining formula
    w j ⁢ ( z ) subscript 𝑤 𝑗 𝑧 {\displaystyle{\displaystyle w_{j}(z)}}
    xml-id
    C2.S7.XMD8.m1adec
    0 references
     
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