Abstract
We derive an expansion for the Riemann zeta function ζ(s) involving incomplete gamma functions with their second argument proportional to n2p, where n is the summation index and p is a positive integer. The possibility is examined of reducing the number of terms below the value Nt (t/2π)1/2 in the finite main sum appearing in asymptotic approximations for ζ(s) on the critical line s = 1 2 + it as t → ∞. It is shown that the expansion corresponding to quadratic dependence on n (p = 1) is the best possible representation of this type for ζ(s).
Original language | English |
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Pages (from-to) | 2973-2984 |
Number of pages | 12 |
Journal | Applied Mathematical Sciences |
Volume | 3 |
Issue number | 60 |
Publication status | Published - 2009 |
Keywords
- Asymptotics
- Zeta function
- Incomplete gamma functions