Chebyshev expansions for Abramowitz functions
The Abramowitz functions \(J_ n(x)=\int^ x_ 0 t^ n \exp(-t^ 2- x/t)dt\), \(n\) integer, are evaluated by using Chebyshev expansions. Since these functions satisfy the stable recurrence \[ 2J_ n(x)=(n-1)J_{n- 2}(x)+xJ_{n-3}(x),\quad n=3,4,\dots, \] only the coefficients to 20 decimal places of the expansions for \(J_ 0,J_ 1\) and \(J_ 2\) are given.
scientific article; zbMATH DE number 89536