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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
DOI: https://doi.org/10.1090/S0025-5718-1973-0324874-X
MathSciNet review: 0324874
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Abstract | References | Similar Articles | Additional Information

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?)

  • [1] M. Abramowitz & I. A. Stegun (Editors), Handbook of Mathematical Functions, With Formulas, Graphs and Mathematical Tables, Nat. Bur. Standards Appl. Math. Ser., 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D. C., 1964. MR 29 #4914. MR 0167642 (29:4914)
  • [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)
  • [3] D. R. Childs, "Reduction of multivariate normal integrals to characteristic form," Biometrika, v. 54, 1967, pp. 293-300. MR 35 #5028. MR 0214177 (35:5028)
  • [4] J. E. Dutt, "A representation of multivariate normal probability integrals by integral transforms," Biometrika. (To appear.) MR 0343477 (49:8218)
  • [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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0324874-X
Keywords: Approximation
Article copyright: © Copyright 1973 American Mathematical Society

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