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Formula:8382

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Digital Library of Mathematical Functions ID 25.11.E15

ζ ⁡ ( s , k ⁢ a ) = k - s ⁢ ∑ n = 0 k - 1 ζ ⁡ ( s , a + n k ) , Hurwitz-zeta 𝑠 𝑘 𝑎 superscript 𝑘 𝑠 superscript subscript 𝑛 0 𝑘 1 Hurwitz-zeta 𝑠 𝑎 𝑛 𝑘 {\displaystyle{\displaystyle\zeta\left(s,ka\right)=k^{-s}\*\sum_{n=0}^{k-1}% \zeta\left(s,a+\frac{n}{k}\right),}}


Constraint(s)

k = 1 , 2 , 3 , … 𝑘 1 2 3 … {\displaystyle{\displaystyle k=1,2,3,\dots}}

Symbols List

  • ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}} : Hurwitz zeta function
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • m 𝑚 {\displaystyle{\displaystyle m}} : nonnegative integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • a 𝑎 {\displaystyle{\displaystyle a}} : real or complex parameter
  • s 𝑠 {\displaystyle{\displaystyle s}} : complex variable
  •  Edit this on Wikidata

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