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Euler-Maclaurin, harmonic sums and Stirling's formula

  • G. J. O. Jameson (a1)
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1. Jameson G. J. O., Euler, Ioachimescu and the trapezium rule, Math. Gaz. 96 (March 2012) pp. 136142.
2. Hardy G. H. and Wright E. M., An introduction to the theory of numbers (5th edn.), Oxford University Press (1979).
3. Olver F. W. J., Asymptotics and special functions, Academic Press (1974).
4. Radmore P. M. and Stephenson G., On a generalisation of the limit definition of the Euler constant, Math. Gaz. 88 (March 2004) pp. 102105.
5. Fowler David, The factorial function: Stirling's formula, Math. Gaz. 84 (March 2000) pp. 4250.
6. Hirschhorn Michael, A new version of Stirling's formula, Math. Gaz. 90 (July 2006) pp. 286292.
7. Artin Emil, Einführung in die Theorie der G ammafunktion, Teubner, Leipzig (1931); English translation: The gamma function, Holt, Rinehart and Winston (1964).
8. Jameson G. J. O., A simple proof of Stirling's formula for the gamma function, Math. Gaz. 99 (March 2015) pp. 6874.
9. Gordon Xavier and Sebah Pascal, The Euler constant γ, accessed December 2014 at http://numbers.computation.free.fr/Constants/Gamma/gamma.html
10. Duane W. De Temple and Shun-Hwa Wang, Half integer approximations for the partial sums of the harmonic series, J. Math. Anal. Appl. 160 (1991) pp. 149156.
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The Mathematical Gazette
  • ISSN: 0025-5572
  • EISSN: 2056-6328
  • URL: /core/journals/mathematical-gazette
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