## Abstract

We derive an expansion for the Riemann zeta function ζ(

*s*) involving incomplete gamma functions with their second argument proportional to*n*, where^{2p}*n*is the summation index and*p*is a positive integer. The possibility is examined of reducing the number of terms below the value*N*(_{t}*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