Contributions to the Analytic Theory of Continued Fractions and Infinite Matrices
Ernst D. Hellinger, Hubert Stanley Wall · Annals of Mathematics · 1943
in which the a, are real and positive, and the b, are complex numbers with nonnegative imaginary parts. In addition, we are concerned with certain infinite matrices connected with this continued fraction. In the earlier investigations of continued fractions of this form, beginning with the classical work of Stieltjes [15]', the b, have been supposed real. For this case, and with some additional restrictions, Stieltjes was able to connect the continued fraction with one or more integrals of the form