Asymptotic Behavior of the Continued Fraction Coefficients of a Class of Stieltjes Transforms Including the Binet Function

Let G(z) be a Stieltjes transform (1.1) G ( z ) =   ∫ 0 ∞ υ ( t ) z + t   d t ,             z ∈ S π   : =   [ z ∈ ℂ   :     |   arg   z |     <     π ] ,       https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072126/15070696-a94f-4da5-a117-8ee069a896b3/content/eq2887.tif"/>