DLMF:23.9.E3 (Q7292)

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DLMF:23.9.E3
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    Statements

    Defining formula
    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},}}
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    DLMF id
    DLMF:23.9.E3
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    constraint
    0 < | z | < | z 0 | 0 𝑧 subscript 𝑧 0 {\displaystyle{\displaystyle 0<|z|<|z_{0}|}}
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    Symbols used
    DLMF:23.2.E5
    Defining formula
    ζ ⁡ ( z ) Weierstrass-zeta-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E5.m2adec
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    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1bdec
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    Q12060
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C23.S1.XMD3.m1bdec
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    Q12056
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C23.S1.XMD7.m1adec
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    Q12073
    Defining formula
    c n subscript 𝑐 𝑛 {\displaystyle{\displaystyle c_{n}}}
    xml-id
    C23.S9.XMD1.m1bdec
    0 references
     
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