DLMF:25.11.E32 (Q7706)

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Language	Label	Description	Also known as
English	DLMF:25.11.E32	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{a}x^{n}\psi\left(x\right)\mathrm{d}x=(-1% )^{n-1}\zeta'\left(-n\right)+(-1)^{n}h(n)\frac{B_{n+1}}{n+1}-\sum_{k=0}^{n}(-1% )^{k}\genfrac{(}{)}{0.0pt}{}{n}{k}h(k)\frac{B_{k+1}(a)}{k+1}a^{n-k}+\sum_{k=0}% ^{n}(-1)^{k}\genfrac{(}{)}{0.0pt}{}{n}{k}\zeta'\left(-k,a\right)a^{n-k},}}

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DLMF:25.11.E32

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{\displaystyle{\displaystyle\Re a>0}}

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

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{\displaystyle{\displaystyle\Re a>0}}

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Defining formula

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

C24.S2.SS1.m1ahdec

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Hurwitz zeta function

Defining formula

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

C25.S11.E1.m2aagdec

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Riemann zeta function

Defining formula

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

C25.S2.E1.m2agdec

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Defining formula

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

C1.S2.SS1.m1aadec

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Defining formula

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

C1.S4.SS4.m1aldec

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psi (or digamma) function

Defining formula

{\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}

C5.S2.E2.m2acdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aldec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1apdec

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Defining formula

{\displaystyle{\displaystyle k}}

C25.S1.XMD1.m1ddec

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Defining formula

{\displaystyle{\displaystyle n}}

C25.S1.XMD3.m1odec

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Defining formula

{\displaystyle{\displaystyle x}}

C25.S1.XMD5.m1mdec

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Defining formula

{\displaystyle{\displaystyle a}}

C25.S1.XMD6.m1aadec

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Defining formula

{\displaystyle{\displaystyle h(n)}}

C25.S11.XMD3.m1dec

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Sitelinks

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