LAUSR

Abstract We extend some results recently obtained by Dan Romik [14] about the Taylor coefficients of the theta function θ 3 ( e − π ) to the case θ 3 ( q ) of a real valued variable 0 q 1 . These results are obtained by carefully studying the properties of the cumulants associated to a Jacobi θ 3 (or discrete normal) distributed random variable. This article also states some integrality conjectures about rational sequences that generalize the one studied by Romik.