DLMF:25.11.E17 (Q7691)

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DLMF:25.11.E17
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    Statements

    Defining formula
    ∂ ∂ ⁡ a ⁡ ζ ⁡ ( s , a ) = - s ⁢ ζ ⁡ ( s + 1 , a ) , partial-derivative 𝑎 Hurwitz-zeta 𝑠 𝑎 𝑠 Hurwitz-zeta 𝑠 1 𝑎 {\displaystyle{\displaystyle\frac{\partial}{\partial a}\zeta\left(s,a\right)=-% s\zeta\left(s+1,a\right),}}
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    DLMF id
    DLMF:25.11.E17
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    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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    s ≠ 0 , 1 𝑠 0 1 {\displaystyle{\displaystyle s\neq 0,1}}
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    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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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.m2ardec
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    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4adec
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    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1afdec
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    Q12161
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C25.S1.XMD6.m1odec
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    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1mdec
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