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Euler-Maclaurin, harmonic sums and Stirling's formula

Published online by Cambridge University Press:  13 March 2015

G. J. O. Jameson
G. J. O. Jameson*
Affiliation:
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, e-mail: g.jameson@lancaster.ac.uk
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Type
Articles
Information
The Mathematical Gazette , Volume 99 , Issue 544 , March 2015 , pp. 75 - 89
Copyright
Copyright © Mathematical Association 2015 

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References

1. Jameson, G. J. O., Euler, Ioachimescu and the trapezium rule, Math. Gaz. 96 (March 2012) pp. 136–142.Google Scholar
2. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (5th edn.), Oxford University Press (1979).Google Scholar
3. Olver, F. W. J., Asymptotics and special functions, Academic Press (1974).Google Scholar
4. Radmore, P. M. and Stephenson, G., On a generalisation of the limit definition of the Euler constant, Math. Gaz. 88 (March 2004) pp. 102–105.Google Scholar
5. Fowler, David, The factorial function: Stirling's formula, Math. Gaz. 84 (March 2000) pp. 42–50.Google Scholar
6. Hirschhorn, Michael, A new version of Stirling's formula, Math. Gaz. 90 (July 2006) pp. 286–292.Google Scholar
7. Artin, Emil, Einführung in die Theorie der G ammafunktion, Teubner, Leipzig (1931); English translation: The gamma function, Holt, Rinehart and Winston (1964).Google Scholar
8. Jameson, G. J. O., A simple proof of Stirling's formula for the gamma function, Math. Gaz. 99 (March 2015) pp. 68–74.Google Scholar
9. Gordon, Xavier and Sebah, Pascal, The Euler constant γ, accessed December 2014 at http://numbers.computation.free.fr/Constants/Gamma/gamma.html Google Scholar
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. 149–156.Google Scholar