DLMF:25.11.E41 (Q7715)

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DLMF:25.11.E41
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    Statements

    Defining formula
    ζ ⁡ ( s , a + 1 ) = ζ ⁡ ( s ) - s ⁢ ζ ⁡ ( s + 1 ) ⁢ a + O ⁡ ( a 2 ) . Hurwitz-zeta 𝑠 𝑎 1 Riemann-zeta 𝑠 𝑠 Riemann-zeta 𝑠 1 𝑎 Big-O superscript 𝑎 2 {\displaystyle{\displaystyle\zeta\left(s,a+1\right)=\zeta\left(s\right)-s\zeta% \left(s+1\right)a+O\left(a^{2}\right).}}
    0 references
    DLMF id
    DLMF:25.11.E41
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    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.m2aandec
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    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aidec
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    Q12161
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C25.S1.XMD6.m1afdec
    0 references
    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1zdec
    0 references
     
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