Riemann Zeta Function. Chi(s)via analytic Continuation inside an infinite Loop

2013/12/10 by Van Malderen, Renaat
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1312.2890

Abstract

The paper deals with the analytic entire function Chi(s) closely related to Riemann Zeta Function Zeta(s). A formula is obtained for Chi(s) essentially within the so-called critical strip. This is achieved by applying Cauchy integral formula to an infinite loop encircling the critical strip. In the obtained formula a remarkable role is played by a special type of complex function known as Incomplete Gamma Function. Numerical examples verifying the obtained formula are included.

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