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Rational approximations, software and test methods for sine and cosine integrals. (English) Zbl 0863.65004
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.
65D20Computation of special functions, construction of tables
33B20Incomplete beta and gamma functions
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