Skip to main content

Analytically Continued Hypergeometric Expression of the Incomplete Beta Function

Results in Mathematics volume 41, pages 394–395 (2002)Cite this article

abstract

The Incomplete Beta Function is rewritten as a Hypergeometric Function that is the analytic continuation of the conventional form, a generalization of the finite series, which simpifies the Stieltjes transform of powers of a monomial divided by powers of a binomial.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

39,95 €

Price includes VAT (Finland)

References

  1. A.P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, Integrals and Series (Gorden and Breach, New York, 1990) v3, p. 466, No. 7.3.1.177.

    MATH  Google Scholar 

  2. Handbook of mathematical functions with formulas, graphs, and mathematical tables, ed M. Abramowitz and I. A. Stegun(National Bureau of Standards, Applied mathematics series, 55, Washington, 1970), p. 263, Nos. 6.6.8, 6.6.2, and 6.6.3; see also K. Pearson, Biometrika 16, 202 (1924); M. J. Tretter and G. W. Walster, SIAM J. Sci. Stat. Comput. 1, 321 (1980); N. M. Temme, SIAM J. Math Anal. 18, 1638 (1987); B. W. Brown and L. B. Levy, ACM Trans. Math. Software 20, 393 (1994); and B. G. S. Doman, Math. Comput. 65, 1283 (1996).

  3. Larry C. Andrews, Special Functions for Engineers and Applied Mathematics, (MacMillan, New York, 1985) p. 70.

    Google Scholar 

  4. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 950, No. 8.391.

    MATH  Google Scholar 

  5. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 1043, No. 9.132.2.

    MATH  Google Scholar 

  6. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 1043, No. 9.131c.

    MATH  Google Scholar 

  7. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 937, No. 8334.3.

    MATH  Google Scholar 

  8. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 1043, No. 9.131b.

    MATH  Google Scholar 

  9. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 290, No. 3.227.2; A. Erdélyi et al., Tables of Integral Transforms, Vol. II (McGraw Hill, New York, 1954), p. 217, No. 10.

    MATH  Google Scholar 

  10. See, for instance, D. B. Sumner, Bull. Am. Math. Soc. 55, 174 (1949); A. Byrne and E. R. Love J. Austral. Math. Soc. 18, 328 (1974) and J. Math. Anal. & Appl. 190, 428 (1995).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University Studies, Portland State University, Portland, OR, 97207-0751, USA

    Jack C. Straton

Authors
  1. Jack C. Straton
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Straton, J.C. Analytically Continued Hypergeometric Expression of the Incomplete Beta Function. Results. Math. 41, 394–395 (2002). https://doi.org/10.1007/BF03322781

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322781

1991 Mathematics Subject Classification

  • 33B20
  • 33C05
  • 44A15

Key Words

  • Incomplete beta function
  • hypergeometric function
  • Stieltjes transforms
  • definite integrals