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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 $Si\left(x\right)$ and cosine integral $Ci\left(x\right)$ with maximal accuracy of 20sf., except near the zeros of $Ci\left(x\right)$ 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 $Si$.
MSC:
 65D20 Computation of special functions, construction of tables 33B20 Incomplete beta and gamma functions
SPECFUN; MACHAR
References:
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