DLMF:25.11.E17 (Q7691): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1afdec

Revision as of 13:39, 2 January 2020

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DLMF:25.11.E17
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    Statements

    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:25.11.E17
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    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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    a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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    ζ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    C25.S11.E1.m2ardec
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    f x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    C1.S5.E3.m4adec
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    x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    C1.S5.E3.m2adec
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    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1afdec
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