DLMF:25.14.E2 (Q7741)

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DLMF:25.14.E2
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    Statements

    Defining formula
    ζ ⁡ ( s , a ) = Φ ⁡ ( 1 , s , a ) , Hurwitz-zeta 𝑠 𝑎 Lerch-Phi 1 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(s,a\right)=\Phi\left(1,s,a\right),}}
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    DLMF id
    DLMF:25.14.E2
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    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    a ≠ 0 , - 1 , - 2 , … 𝑎 0 1 2 … {\displaystyle{\displaystyle a\neq 0,-1,-2,\dots}}
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    Symbols used
    Hurwitz zeta function
    Defining formula
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2adec
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    Lerch’s transcendent
    Defining formula
    Φ ⁡ ( z , s , a ) Lerch-Phi 𝑧 𝑠 𝑎 {\displaystyle{\displaystyle\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S14.E1.m2aadec
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