Rational approximations, software and test methods for sine and cosine integrals
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Rational approximations to the sine integralSi(x) and cosine-integralCi(x) are developed which give an accuracy of 20sf. The robust construction of software for these functions is discussed, together with a test procedure for assessing the performance of such codes. Use of the tests discovers a major error in the netlib library FN codes forSi. Fortran versions of the codes and tests are available by electronic mail.
KeywordsSine-integral cosine-integral rational software testing
Subject classification65D20 65V05 41A20 33A10
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- M. Abramowitz and I.A. Stegun (eds.),Handbook of Mathematical Functions, Dover, New York, 1965.Google Scholar
- C.W. Clenshaw, The numerical solution of linear differential equations in Chebyshev series, Proc. Camb. Phil. Soc. 53 (1957) 134–149.Google Scholar
- W.J. Cody, W. Fraser and J.F. Hart, Rational Chebyshev approximation using linear equations, Numer. Math. 12 (1968) 242–251.Google Scholar
- W. Gautschi, Computation of successive derivatives off(z)/z, Math. Comp. 20 (1966) 209–214.Google Scholar
- J.F. Hart, E.W. Cheney, C.L. Lawson, H.J. Maehhly, C.K. Mesztenyi, J.R. Rice, H.G. Thacher and C. Witzgall,Computer Approximations, Wiley, New York, 1968.Google Scholar