Far East J.Appl.Math. 32(1) (2008), 1-11 MONTAGE FOR THE GAMMA FUNCTION

The ln(z) consists of three parts, (i) (z 12) ln z z, (ii) the constant ln p 2, and (iii) the Stieltjes continued fraction J(z). The partial numerators for J(z) have been found by Char (Mathematics of Computation, 34(150), 1980) and asymptotic forms are needed, along with a conjecture of Stieltjes. Sequences of approximants are set up for ln p 2. In another direction we use a second order continued fraction for the exponential function ez, noting that ddz e z = ez so that a derivative of a continued fraction is involved