World Scientific
  • Search
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
Our website is made possible by displaying certain online content using javascript.
In order to view the full content, please disable your ad blocker or whitelist our website

System Upgrade on Tue, Oct 25th, 2022 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at [email protected] for any enquiries.

Asymptotics of certain sums required in loop regularisation by:3 (Source: Crossref)

    We consider the three conjectures stated in a 2003 paper of Wu, concerning the asymptotics of particular sums of products of binomials, powers and logarithms. These sums relate to the form of the regularised integrals used in loop regularisation. We show all three are true, extend them to more general powers and produce their full asymptotic series. We also extend a classical result to produce an exact formula for the sum in the last.

    PACS: 02.30.Mv, 11.15.Bt


    • 1. S. Weinberg, The Quantum Theory of Fields (Cambridge Univ. Press, 1995). CrossrefGoogle Scholar
    • 2. G. B. Folland, Quantum Field Theory: A Tourist Guide for Mathematicians (Amer. Math. Soc., 2008). CrossrefGoogle Scholar
    • 3. W. Pauli, Scientific Correspondence with Bohr, Einstein, Heisenberg, a.o., Sources in the History of Mathematics and Physical Sciences, Vol. III (Springer-Verlag, 1993), pp. 609–621. CrossrefGoogle Scholar
    • 4. (Eds.) G. VeloA. S. Wightman, Renormalization Theory (D. Reidel, 1976). CrossrefGoogle Scholar
    • 5. Y. Wu, Int. J. Mod. Phys. A 18, 5363 (2003). Link, ISI, ADSGoogle Scholar
    • 6. Y.-L. Ma and Y.-L. Wu, Int. J. Mod. Phys. A 21, 6383 (2006). Link, ISI, ADSGoogle Scholar
    • 7. Y.-B. Dai and Y.-L. Wu, Eur. Phys. J. C 39, 1 (2005). Crossref, ISI, ADSGoogle Scholar
    • 8. J.-W. Cui and Y.-L. Wu, Int. J. Mod. Phys. A 23, 2861 (2008). Link, ISI, ADSGoogle Scholar
    • 9. J.-W. Cui, Y.-L. Ma and Y.-L. Wu, Phys. Rev. D 84, 025020 (2011). Crossref, ISI, ADSGoogle Scholar
    • 10. Y.-L. Wu, Int. J. Mod. Phys. A 29, 1430007 (2014). Link, ISI, ADSGoogle Scholar
    • 11. D. Huang, Y. Tang and Y.-L. Wu, Commun. Theor. Phys. 7, 427 (2012). Crossref, ISI, ADSGoogle Scholar
    • 12. Y. Wu, Mod. Phys. Lett. A 19, 2191 (2004). Link, ISI, ADSGoogle Scholar
    • 13. L. Euler, Novi Commentarii Academiae Scientiarum Petropolitanae 13, 3 (1769), reprinted in Opera Omnia, Vol. I.28, pp. 41–98 [E368]. Google Scholar
    • 14. L. Euler, Institutiones Calculi Differentialis cum eius usu in analysi finitorum AC doctrina serierum (St. Petersburg, 1755), reprinted in Opera Omnia, Vol. I.10 [E212]. Google Scholar
    • 15. H. W. Gould, Amer. Math. Monthly 85, 450 (June–July 1978). Crossref, ISIGoogle Scholar
    • 16. R. Wong, Asymptotic Approximations of Integrals (Society for Industrial and Applied Mathematics, 2001). CrossrefGoogle Scholar
    • 17. L. Euler, Nova Acta Academiae Scientarum Imperialis Petropolitinae 15, 33 (1806), reprinted in Opera Omnia, Vol. I.16, pp. 104–116 [E726]. Google Scholar
    • 18. R. P. Stanley, Enumerative Combinatoric, Vol. 2 (Cambridge Univ. Press, 1999). CrossrefGoogle Scholar
    • 19. G. H. Hardy, A Course in Pure Mathematics (Cambridge Univ. Press, 1948). Google Scholar
    • 20. A. Erdélyi, Asymptotic Expansions (Dover, 1956). Google Scholar
    Remember to check out the Most Cited Articles!

    Boost your collection with these new physics books today!