Asymptotic behavior of the inverse of tails of Hurwitz zeta function
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This paper deals with the inverse of tails of Hurwitz zeta function. More precisely, for any positive integer $s\geq2$ and {$0\leq a<1$}, we give an algorithm for finding a simple form of {$f_{s,a}(n)$} such that $$ \lim_{n\rightarrow\infty}\left\{\left(\sum^\infty_{k=n}\frac{1}{(k+a)^s}\right)^{-1}-{f_{s,a}(n)}\right\}=0. $$ We show that {$f_{s,a}(n)$} is a polynomial in $n-a$ of order $s-1$. All coefficients of {$f_{s,a}(n)$} are represented in terms of Bernoulli numbers.
Abstract
This paper deals with the inverse of tails of Hurwitz zeta function. More precisely, for any positive integer $s\geq2$ and {$0\leq a<1$}, we give an algorithm for finding a simple form of {$f_{s,a}(n)$} such that $$ \lim_{n\rightarrow\infty}\left\{\left(\sum^\infty_{k=n}\frac{1}{(k+a)^s}\right)^{-1}-{f_{s,a}(n)}\right\}=0. $$ We show that {$f_{s,a}(n)$} is a polynomial in $n-a$ of order $s-1$. All coefficients of {$f_{s,a}(n)$} are represented in terms of Bernoulli numbers.
참고문헌 (7)
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