On the growth of meromorphic functions defined by quasi-regular c-fractions

We investigate the growth of the meromorphic function defined by 1 + a1zb + a2z1 + … , where ai are complex numbers, ai ≠ 0, ¦ai¦ ⩾ ¦ai+1¦ (i = 1, 2, …) and limi→∞ ai =0. b is a complex number.