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September, 1963 Chebyshev Polynomial and Other New Approximations to Mills' Ratio
W. D. Ray, A. E. N. T. Pitman
Ann. Math. Statist. 34(3): 892-902 (September, 1963). DOI: 10.1214/aoms/1177704012


For various but sound practical reasons it has become desirable to approximate to previously tabulated mathematical functions by polynomials or rational fractions. In this paper Chebyshev polynomials are used to approximate Mills' Ratio over two separate ranges [0, 1], [1, $\infty$] of the argument. Some new asymptotic expansions for this ratio are also obtained by an extended use of the symbolic operator method, revealing incidentally that Ruben's (1962) expansion is a special but not necessarily superior case.


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W. D. Ray. A. E. N. T. Pitman. "Chebyshev Polynomial and Other New Approximations to Mills' Ratio." Ann. Math. Statist. 34 (3) 892 - 902, September, 1963.


Published: September, 1963
First available in Project Euclid: 27 April 2007

zbMATH: 0146.41005
MathSciNet: MR153101
Digital Object Identifier: 10.1214/aoms/1177704012

Rights: Copyright © 1963 Institute of Mathematical Statistics

Vol.34 • No. 3 • September, 1963
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