Number Theory


Analysis of the Matrix Xjk=[x(j,k)] ∈C Where X(j,k)=δ+ω(α+βj)^φk

Authors: Pedro Caceres

The function x(j,k)=δ+ω(α+βj)^φk in C→C is a generalization of the power function y(α)=α^k in R→R and the exponential function y(k)=α^k in R→R. In this paper we are going to calculate the values of infinite and partial sums and products involving elements of the matrix Xjk=[x(j,k)]∈C As a result, several new representations will be made for some infinite series, including the Riemann Zeta Function in C.

Comments: 56 Pages.

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Submission history

[v1] 2018-02-22 00:31:26

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