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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The efficient calculation of the incomplete beta-function ratio for half-integer values of the parameters $a, b$
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by A. R. DiDonato and M. P. Jarnagin PDF
Math. Comp. 21 (1967), 652-662 Request permission
References
  • Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 1964. For sale by the Superintendent of Documents. MR 0167642
  • Harald CramΓ©r, Mathematical Methods of Statistics, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946. MR 0016588
  • A. R. DiDonato & M. P. Jarnagin, "A method for computing the incomplete beta function ratio," NWL Report 1949 (revised), U. S. Naval Weapons Lab., Dahlgren, Virginia, 1966.
  • Henry E. Fettis, On the calculation of integrals of the form $\int ^\theta _0\sin ^p\phi \cos ^q\phi d\phi$, J. Math. Physics 33 (1954), 283–289. MR 0064484
  • W. Gautschi, "Incomplete beta function ratios," Comm. ACM, v. 7, 1964, p. 143.
  • F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1956. MR 0075670
  • O. Ludwig, "Incomplete beta ratio," Comm. ACM, v. 6, 1963, p. 314. E. C. Molina, "Expansions for Laplacian integrals of the form $\smallint _{{x_1}}^{{x_2}}{[y(t)]^\theta }\Phi (t)dt$," Bell. System Tech. J., v. 11, 1932, p. 563.
  • Karl Pearson (ed.), Tables of the incomplete beta-function, Published for the Biometrika Trustees by Cambridge University Press, London, 1968. Originally prepared under the direction of and edited by Karl Pearson; Second edition with a new introduction by E. S. Pearson and N. L. Johnson. MR 0226815
  • H. E. Soper, The Numerical Evaluation of the Incomplete B-Function or of the Integral $\smallint _0^x{x^{p - 1}}{(1 - x)^{q - 1}}dx$ for Ranges of x Between 0 and 1, Tracts for Computers, No. VII, Cambridge Univ. Press, New York, 1921. I. C. Tang, "On the computation of a certain type of incomplete beta functions," Comm. ACM, v. 6, 1963, p. 689.
  • Catherine M. Thompson, Tables of percentage points of the incomplete beta-function, Biometrika 32 (1941), 151–181. MR 5429, DOI 10.2307/2332208
  • Francesco Giacomo Tricomi, Equazioni differenziali, Manuali: Serie di matematica, Paolo Boringhieri, Torino, 1961 (Italian). 3a ed. riveduta e ampliata. MR 0138811
  • M. E. Wise, The incomplete beta function as a contour integral and a quickly converging series for its inverse, Biometrika 37 (1950), 208–218. MR 40622, DOI 10.1093/biomet/37.3-4.208
  • M. E. Wise, The incomplete beta function and the incomplete gamma function: An acknowledgment, J. Roy. Statist. Soc. Ser. B 10 (1948), 264. MR 28475, DOI 10.1111/j.2517-6161.1948.tb00016.x
  • M. E. Wise, The use of the negative binomial distribution in an industrial sampling problem, Suppl. J. Roy. Statist. Soc. 8 (1946), 202–211. MR 21289, DOI 10.2307/2983562
  • J. Wishart, "Determination of $\smallint _0^\theta {\cos ^{n + 1}}\theta d\theta$ for large values of $n$, and its application to the probability integral of symmetrical frequency curves," Biometrika, v. 17, 1925, pp. 68, 469.
  • Tables of the cumulative binomial probability distribution, The Annals of the Computation Laboratory of Harvard University, vol. 35, Harvard University Press, Cambridge, Mass., 1955. MR 0082203
  • Tables of the Binomial Probability Distribution, National Bureau of Standards Applied Mathematics Series, No. 6, U.S. Government Printing Office, Washington, D.C., 1950. MR 0035108
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Additional Information
  • © Copyright 1967 American Mathematical Society
  • Journal: Math. Comp. 21 (1967), 652-662
  • MSC: Primary 65.20
  • DOI: https://doi.org/10.1090/S0025-5718-1967-0221730-X
  • MathSciNet review: 0221730