The incomplete beta function and its ratio to the complete beta function

Authors:
David Osborn and Richard Madey

Journal:
Math. Comp. **22** (1968), 159-162

DOI:
https://doi.org/10.1090/S0025-5718-68-99888-8

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Abstract | References | Additional Information

Abstract: The incomplete beta function, , and its ratio to the complete beta function 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 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 and another for . 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 values.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-68-99888-8

Article copyright:
© Copyright 1968
American Mathematical Society