Special Function: Functions that arise in the solution of specific differential equations or in mathematical physics, noted for their distinctive properties and recurrence relations.

D. J. Allwright, Hypergraphic Functions and Bifurcations in Recurrence Relations, SIAM Journal on Applied Mathematics, Vol. 34, No. 4 (Jun., 1978), pp. 687-691 ...

We consider positive powers of a rational generating function F(x, z) of the variable z whose numerator has degree at most 1, denominator has degree 2, and where coefficients are functions of x. Many ...