Formula:DLMF:25.2:E9

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formula in Definition and Expansions

Formula:DLMF:25.2:E10 >>

Proof

Follows from

$$

by repeated integration by parts.

Symbols List

& : logical and
$\zeta$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
$\mathrm{\Sigma }$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
$(\genfrac{}{}{0ex}{}{n}{k})$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
$B_n$ : Bernoulli polynomial : http://dlmf.nist.gov/24.2#i
$\int$ : integral : http://dlmf.nist.gov/1.4#iv
${\tilde{B}}_n$ : periodic Bernoulli functions : http://dlmf.nist.gov/24.2#iii
${\mathrm{d}}^{n}x$ : differential : http://dlmf.nist.gov/1.4#iv
$\mathrm{\Re }z$ : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation (9), Section 25.2 of DLMF.

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