Statistical encounters with complex B-splines

Complex B-splines as introduced in Forster et al. (Appl. Comput. Harmon. Anal. 20:281-282, 2006) are an extension of Schoenberg's cardinal splines to include complex orders. We exhibit relationships between these complex B-splines and the complex analogues of the classical difference and divided difference operators and prove a generalization of the Hermite-Genocchi formula. This generalized Hermite-Genocchi formula then gives rise to a more general class of complex B-splines that allows for some interesting stochastic interpretations.