Date: Sun, 12 Feb 95 19:04:02 +0000 Here is the transcription of algorithm #6 of Collected Algorithms from CACM. I substituted greek letters by their names, the multiplicative operator by * and the potentiation (x raised to y) by ^ (x ^ y). jr Jose R. Valverde European Bioinformatics Institute txomsy@ebi.ac.uk -------------------------------------------------------------------------- 6. BESSEL FUNCTION I, ASYMPTOTIC EXPANSION Dorothea S. Clarke General Electric Co., FPLD, Cincinnati 15, Ohio comment Compute the Bessel Function In(X) when n and X are within the bounds of the asymptotic expansion. The procedure calling statement gives n, X and an absolute tolerance delta for determining the point at which the terms of the summation become in- significant; procedure I(n, X, delta) =: (IA) begin I: r := 1 ; pe := (4 * (n^2) - 1) / (8 * X) sum := - pe Repeat: r := r + 1 pe := pe * (((2 * n)^2) - ((2 * r - 1)^2)) / (r * 8 * X) if (delta < abs(pe)) begin sum := sum + ((-1)^r) * pe ; go to Repeat end IA := (1 + sum) * (exp(X) / sqrt(2 * PI * X)) return end