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31: Bibliography L

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A table of integrals involving the functions $E_n(x)$ .

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Notes:

National Research Council of Canada, Division of Atomic Energy, Document no. MT-131 (NRC 1553)

Referenced by:

§8.19(x).

Encodings:

BibTeX

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32: 25.11 Hurwitz Zeta Function

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25.11.15 $$\zeta (s,ka)=k^{-s}\sum _{n=0}^{k-1}\zeta (s,a+\frac{n}{k}),$$ $s\ne 1$, $k=1,2,3,\mathrm{\dots }$.

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Symbols:

$\zeta (s,a)$: Hurwitz zeta function, $k$: nonnegative integer, $m$: nonnegative integer, $n$: nonnegative integer, $a$: real or complex parameter and $s$: complex variable

Keywords:

special value

Proof sketch:

Derivable by starting with (25.11.1), replacing $a\mapsto ka$, pulling out a factor of $k^{-s}$ and performing a change of sum index $n=km+l$ with $m\ge 0$ and $0\le l\le k-1$, which through Euclidean division converts the single sum into a double sum of the correct form.

Referenced by:

(25.11.24)

Permalink:

http://dlmf.nist.gov/25.11.E15

Encodings:

pMML, png, TeX

See also:

Annotations for §25.11(v), §25.11 and Ch.25

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