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Mathematics of Computation

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New approximations to familiar functions

Authors: J. E. Dutt, T. K. Lin and L. C. Tao
Journal: Math. Comp. 27 (1973), 939-942
MSC: Primary 65D15
MathSciNet review: 0324874
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Abstract: Using an integral representation of the Hermite polynomial and then Gaussian quadrature, very accurate representations are obtained for $ \exp ( - {z^2}),{\operatorname{erf}}(z)$, and $ \arcsin (z)$.

References [Enhancements On Off] (What's this?)

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  • [2] R. Bellman, B. G. Kashef & R. Vasudevan, "A useful approximation to $ \exp ( - {t^2})$," Math. Comp., v. 26, 1972, pp. 233-235. MR 0298884 (45:7933)
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  • [5] J. E. Dutt, The Evaluation of an Integral Involving Marcum's Q Function, Columbia University, Electronics Research Laboratories, Research Note N-6/180, 1962.
  • [6] K. S. Miller, Multidimensional Gaussian Distributions, SIAM Ser. Appl. Math., Wiley, New York, 1964. MR 30 #1564. MR 0171333 (30:1564)

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Keywords: Approximation
Article copyright: © Copyright 1973 American Mathematical Society

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