confluent hypergeometric function

_0 F_1(;a;z) congruent lim_(q->∞) _1 F_1(q;a;z/q). It has a series expansion _0 F_1(;a;z) = sum_(n = 0)^∞ z^n/((a)_n n!) and satisfies z(d^2 y)/(d z^2) + a(d y)/(d z) - y = 0. It is implemented in the Wolfram Language as Hypergeometric0F1[b, z].

confluent hypergeometric function of the first kind | generalized hypergeometric function | hypergeometric function