An expansion of the Riemann Zeta function on the critical line

Overview & Synopsis

We give an expansion of the Riemann zeta function on the critical line as a converging series m≥0 a m q m (1 2 + it) in the space L 2 (R, dt cosh(πt)), where the functions q m are related to Meixner polynomials of the first kind and the coefficients a m are linear combinations of the Euler constant γ and the values ζ(2), ζ(3),. .. , ζ(m + 1).