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Talk: The connection between the Riemann Zeta function and the Legendre polynomials

The connection between the Riemann Zeta function and the Legendre polynomials

Date: 2012..12..28
Event: International Conference on Mathematical Sciences 2012. The 125th Birth Anniversary celebrations of Srinivasa Ramanujam
Venue: Nagpur, India

Abstract

In this talk we present all the theory developed during the last years about the Riemann Zeta function, the connection between the the irrationality proof of $$\zeta(2)$$ and $$\zeta(3)$$ and the Legendre polynomials, we also discuss about the irrationality of $$\zeta(2n+1)$$ and its connection with the Legendre polynomials presenting infinitely many integral sequences converging to such values as fast as we want. We also present analogous results of the results mentioned above for a $$q$$-analog of the Zeta function and its connection with the $$q$$-Leguendre polynomials.