This paper is published in Volume-5, Issue-4, 2019
Area
Mathematics
Author
Org/Univ
Al-Beroni University, Afghanistan, Afghanistan
Pub. Date
06 August, 2019
Paper ID
V5I4-1274
Publisher
Keywords
Riemann zeta function, Analytic continuation, Gamma function, Jacobi theta function, Xi function.

#### Citationsacebook

IEEE
Mohammad Haroon Sabiri. Analytic continuation of Riemann zeta function, International Journal of Advance Research, Ideas and Innovations in Technology, www.IJARIIT.com.

APA
Mohammad Haroon Sabiri (2019). Analytic continuation of Riemann zeta function. International Journal of Advance Research, Ideas and Innovations in Technology, 5(4) www.IJARIIT.com.

MLA
Mohammad Haroon Sabiri. "Analytic continuation of Riemann zeta function." International Journal of Advance Research, Ideas and Innovations in Technology 5.4 (2019). www.IJARIIT.com.

#### Abstract

In this paper, we present Riemann zeta function and its analytic continuation and functional equation. We will begin with the Gamma function and some properties of the Gamma function. Then we prove that the Riemann zeta function can be represented by Euler’s product. We will present proof of analytic continuation of the zeta function using Gamma function. Also, we define a Jacobi Theta function and Xi function with the proof of its functional equation and then it will be used to prove the analytic continuation of zeta function as well as its functional equation.
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