 By the ratio test, this series converges absolutely for all "z" and "n", and uniformly for all regions with bounded |"z"|, and hence the Bessel–Clifford function is an entire function of the two complex variables "n" and "z".It follows from the above series on differentiating with respect to "x" that formula_3 satisfies the linear second-order homogeneous differential equation

This equation is of generalized hypergeometric type, and in fact the Bessel–Clifford function is up to a scaling factor a Pochhammer–Barnes hypergeometric function; we have

Unless n is a negative integer, in which case the right hand side is undefined, the two definitions are essentially equivalent; the hypergeometric function being normalized so that its value at "z" = 0 is one.The Bessel function of the first kind can be defined in terms of the Bessel–Clifford function as

when "n" is not an integer we can see from this that the Bessel function is not entire.