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

Renaat Van Malderen

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arXiv · 1312.2890

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

Renaat Van Malderen

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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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Renaat Van Malderen. 2013-12-10. Riemann Zeta Function. Chi(s)via analytic Continuation inside an infinite Loop. https://arxiv.org/abs/1312.2890

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