Numerical calculation of the generalized sine and cosine integral. (Q1415050)

This paper concerns the efficient calculation of \[ \text{Si}(x, a)= \int^x_0 t^{-a}\sin t\,dt,\quad 0< a< 2, \] and \[ \text{Ci}(x, a)= \int^x_0 t^{-a} \cos t\,dt,\quad 0< a< 1, \] investigated in detail by the reviewer [Acta Math. 85, 117--181 (1951; Zbl 0042.30304), Acta Math. 89, 107--131 (1953; Zbl 0050.07305)] suitable when a great number of function evaluations is needed as for aircraft simulation. The evaluation is based on (truncated) Chebyshev series for sine and cosine, first in the range \(0< x\leq\lambda\) and then for \(\lambda< x<\infty\) with \(\lambda\) suitably determined.