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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.

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The incomplete beta function and its ratio to the complete beta function
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by David Osborn and Richard Madey PDF
Math. Comp. 22 (1968), 159-162 Request permission

Abstract:

The incomplete beta function, ${B_x}(p,q) = \int {_0^x} {y^{p - 1}}{(1 - y)^{q - 1}}dy$, and its ratio to the complete beta function ${B_1}(p,q)$ has been calculated on an IBM-7044 computer to five significant figures and tabulated for the arguments p and q each in the interval from 0.5 to 2.0 with increments of 0.05 and for the parameter $x$ in the interval 0.1 to 1.0 with increments of 0.01. The function was evaluated by first expanding a factor of the integrand in a binomial series and then integrating each term. In order to facilitate computation, one expansion is taken for $x \leqq 1/2$ and another for $1/2 < x \leqq 1$. The expansions are truncated when the relative error is less than or equal to an arbitrarily predetermined fraction. Typical running time for achieving five significant figures on the IBM-7044 is about one minute for ${10^4}$ values.
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Additional Information
  • © Copyright 1968 American Mathematical Society
  • Journal: Math. Comp. 22 (1968), 159-162
  • DOI: https://doi.org/10.1090/S0025-5718-68-99888-8