Summary: An asymptotic formula for the zeros, \(z_n\), of the entire function \(e_q(x)\) for \(q\ll 1\) is obtained. As \(q\) increases above the first collision point at \(q^*_1\approx 0.14\), these zeros collide in pairs and then move off into the complex \(z\) plane. They move off as (and remain) a complex conjugate pair. The zeros of the ordinary higher derivatives and of the ordinary indefinite integrals of \(e_q(x)\) vary with \(q\) in a similar manner. Properties of \(e_q(z)\) for \(z\) complex and for arbitrary \(q\) are deduced. For \(0\leq q< 1\), \(e_q(z)\) is an entire function of order 0. By the Hadamard-Weierstrass factorization theorem, infinite product representations are obtained for \(e_q(z)\) and for the reciprocal function \(e^{- 1}_q(z)\). If \(q\neq 1\), the zeros satisfy the sum rule \(\sum^\infty_{n= 1} (1/ z_n)= -1\).