_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]. A Bessel function of the first kind can be expressed in terms of this function by J_n(x) = (1/2 x)^n/(n!) _0 F_1(;n + 1; - 1/4 x^2) (Petkovšek et al. 1996).
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