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The value of an integral in Gradshteyn and Ryzhik’s table

  • Juan Arias de ReynaEmail author
Article
  • 34 Downloads

Abstract

In 2010, V. H. Moll observed that entry 3.248.5 in the sixth edition of Gradshteyn and Ryzhik’s table of integrals was incorrect, and he asked for the value of the integral. We evaluate the integral in terms of two elliptic integrals. The evaluation is standard but involved, using real and complex analysis.

Keywords

Definite integrals Elliptic integrals Complex analysis 

Mathematics Subject Classification

26A42 30E20 28A99 33E05 

Notes

References

  1. 1.
    Amdeberhan, T., Moll, V.: The integrals in Gradshteyn and Ryzhik. Part 14: an elementary evaluation of entry 3.411.5. Sci. Ser. A Math. Sci. (N.S.) 19, 97–103 (2010)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Bailey, D.H., Borwein, J.M., Calkin, N.J., Girgensohn, R., Luke, D.R., Moll, V.: Experimental Mathematics in Action. A K Peters Ltd, Wellesley, MA (2007)CrossRefGoogle Scholar
  3. 3.
    Boros, G., Moll, V., Riley, S.: An elementary evaluation of a quartic integral. Sci. Ser. A Math. Sci. (N.S.) 11, 1–12 (2005)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Byrd, P.F., Friedman, M.D.: Handbook of Elliptic Integrals for Engineers and Scientist, 2nd edn. Springer, Berlin (1971). RevisedCrossRefGoogle Scholar
  5. 5.
    Gradshteyn, I.S.: Table of Integrals, Series, and Products. Edited by Jeffrey, A., Zwillinger, D., 6th edn. Academic Press, New York (2000)Google Scholar
  6. 6.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Edited by Jeffrey, A., Zwillinger, D., 7th edn, Academic Press, New York (2007)Google Scholar
  7. 7.
    Moll, V.: Seized opportunities. Not. Am. Math. Soc. 57(4), 476–484 (2010)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Moll, V.: Special Integrals of Gradshteyn and Ryzhik: The Proofs, vol. 1. CRC Press, Boca Raton, FA (2015)CrossRefGoogle Scholar
  9. 9.
    Moll, V.: Special Integrals of Gradshteyn and Ryzhik: The Proofs, vol. II. CRC Press, Boca Raton, FA (2016)zbMATHGoogle Scholar
  10. 10.
    NIST Digital Library of Mathematical Functions. Olver, F.W.J., Olde Daalhuis, A.B., Lozier, D.W., Schneider, B.I., Boisvert, R.F., Clark, C.W., Miller, B.R., Saunders, B.V. (eds.). http://dlmf.nist.gov/
  11. 11.
    Whittaker, E.T., Watson, G.N.: A Course in Modern Analysis, 4th edn. Cambridge University Press, New York (1965)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Facultad de MatemáticasUniv. de SevillaSevilleSpain

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