DLMF:23.9.E3 (Q7292): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: DLMF:23.2.E5 / rank
 
Normal rank
Property / Symbols used: DLMF:23.2.E5 / qualifier
 
Defining formula:

ζ ( z ) Weierstrass-zeta-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}

\Weierstrasszetalatt@@{\NVar{z}}{\NVar{\mathbb{L}}}
Property / Symbols used: DLMF:23.2.E5 / qualifier
 
xml-id: C23.S2.E5.m2adec
Property / Symbols used
 
Property / Symbols used: Q12055 / rank
 
Normal rank
Property / Symbols used: Q12055 / qualifier
 
Defining formula:

𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}

\mathbb{L}
Property / Symbols used: Q12055 / qualifier
 
xml-id: C23.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12060 / rank
 
Normal rank
Property / Symbols used: Q12060 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12060 / qualifier
 
xml-id: C23.S1.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12056 / rank
 
Normal rank
Property / Symbols used: Q12056 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12056 / qualifier
 
xml-id: C23.S1.XMD7.m1adec
Property / Symbols used
 
Property / Symbols used: Q12073 / rank
 
Normal rank
Property / Symbols used: Q12073 / qualifier
 
Defining formula:

c n subscript 𝑐 𝑛 {\displaystyle{\displaystyle c_{n}}}

c_{n}
Property / Symbols used: Q12073 / qualifier
 
xml-id: C23.S9.XMD1.m1bdec

Latest revision as of 15:57, 2 January 2020

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DLMF:23.9.E3
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    Statements

    ζ ( z ) = 1 z - n = 2 c n 2 n - 1 z 2 n - 1 , Weierstrass-zeta-on-lattice 𝑧 𝕃 1 𝑧 superscript subscript 𝑛 2 subscript 𝑐 𝑛 2 𝑛 1 superscript 𝑧 2 𝑛 1 {\displaystyle{\displaystyle\zeta\left(z\right)=\frac{1}{z}-\sum_{n=2}^{\infty% }\frac{c_{n}}{2n-1}z^{2n-1},}}
    0 references
    DLMF:23.9.E3
    0 references
    0 < | z | < | z 0 | 0 𝑧 subscript 𝑧 0 {\displaystyle{\displaystyle 0<|z|<|z_{0}|}}
    0 references
    ζ ( z ) Weierstrass-zeta-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}
    C23.S2.E5.m2adec
    0 references
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    C23.S1.XMD1.m1bdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C23.S1.XMD3.m1bdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C23.S1.XMD7.m1adec
    0 references
    c n subscript 𝑐 𝑛 {\displaystyle{\displaystyle c_{n}}}
    C23.S9.XMD1.m1bdec
    0 references