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Zbl 0863.65004
MacLeod, Allan J.
Rational approximations, software and test methods for sine and cosine integrals. (English)
[J] Numer. Algorithms 12, No.3-4, 259-272 (1996). ISSN 1017-1398; ISSN 1572-9265/e

The present work develops suitable rational approximations to the sine integral $Si(x)$ and cosine integral $Ci(x)$ with maximal accuracy of 20sf., except near the zeros of $Ci(x)$ for $x>6$. The implementation of these approximations into a robust and reliable code is then considered. Finally, a test procedure, to assess the performance of $Si$ and $Ci$ codes, is developed and applied to various available programs. Use of the tests discovers a major error in the netlib for codes for $Si$.
[R.S.Dahiya (Ames)]

MSC 2000:: *65D20 Computation of special functions
33B20 Incomplete beta and gamma functions

Keywords: software; rational approximations; sine integral $Si(x)$; cosine integral $Ci(x)$; test procedure; performance

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