Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ASYMPTOTIC BEHAVIOR OF THE INVERSE OF TAILS OF HURWITZ ZETA FUNCTION

  • Lee, Ho-Hyeong (Department of Mathematics and Research Institute for Basic Sciences Kyung Hee University) ;
  • Park, Jong-Do (Department of Mathematics and Research Institute for Basic Sciences Kyung Hee University)
  • Received : 2019.11.24
  • Accepted : 2020.02.19
  • Published : 2020.11.01
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Abstract

This paper deals with the inverse of tails of Hurwitz zeta function. More precisely, for any positive integer s ≥ 2 and 0 ≤ a < 1, we give an algorithm for finding a simple form of fs,a(n) such that $$\lim_{n{\rightarrow}{\infty}}\{\({\sum\limits_{k=n}^{\infty}}{\frac{1}{(k+a)^s}}\)^{-1}-f_{s,a}(n)\}=0$$. We show that fs,a(n) is a polynomial in n-a of order s-1. All coefficients of fs,a(n) are represented in terms of Bernoulli numbers.

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References

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