DLMF:25.11.E7 (Q7681): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:25.11.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\zeta\left(s,a\right)=\frac{1}{a^{s}}+\frac{1}{(1+% a)^{s}}\left(\frac{1}{2}+\frac{1+a}{s-1}\right)+\sum_{k=1}^{n}\genfrac{(}{)}{0% .0pt}{}{s+2k-2}{2k-1}\frac{B_{2k}}{2k}\frac{1}{(1+a)^{s+2k-1}}-\genfrac{(}{)}{% 0.0pt}{}{s+2n}{2n+1}\int_{1}^{\infty}\frac{\widetilde{B}_{2n+1}\left(x\right)}% {(x+a)^{s+2n+1}}\mathrm{d}x,}}

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DLMF:25.11.E7

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{\displaystyle{\displaystyle\Re s>-2n}}

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{\displaystyle{\displaystyle n=1,2,3,\dots}}

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{\displaystyle{\displaystyle\Re s>-2n}}

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Defining formula

{\displaystyle{\displaystyle B_{\NVar{n}}}}

C24.S2.SS1.m1aadec

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Hurwitz zeta function

Defining formula

{\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}

C25.S11.E1.m2ahdec

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Defining formula

{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

C1.S2.SS1.m1adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1abdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abdec

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Defining formula

{\displaystyle{\displaystyle\widetilde{B}_{\NVar{n}}\left(\NVar{x}\right)}}

C24.S2.SS3.m1aadec

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