Recursive relations among maximally flat fractional delay FIR filters

In this paper we provide some analytical results of maximally flat fractional delay finite impulse response filters. First, we represent their transfer functions in terms of the Gauss hypergeometric function. Secondly, we derive the generating function of these transfer functions. Finally, we provide recursive relations among transfer functions. The recursions are derived from the method of undetermined coefficients. In the appendix, we list some three-term recursive relations.