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An Approximation connected with e-x

Published online by Cambridge University Press:  20 January 2009

E. T. Copson
E. T. Copson
Affiliation:
St Andrews University.
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One of the many interesting problems discussed by Ramanujan is concerned with the effect of truncating at its maximum term nn/n! the exponential series for en, where n is a positive integer. When n is large, the sum of the first n terms is, roughly speaking, half the sum of the whole series.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 3 , Issue 3 , February 1933 , pp. 201 - 206
Copyright
Copyright © Edinburgh Mathematical Society 1933

References

page 201 note 1 Collected Papers of Srinivasa Ramanujan (1927), xxvi.Google Scholar

page 201 note 2 Journal London Math. Soc., 3 (1928), 225–232.Google Scholar

page 201 note 3 Proc. London Math. Soc., (2), 29 (1928), 293–308.Google Scholar

page 203 note 1 Bromwich, Infinite Series (1926), 485.Google Scholar

page 203 note 2 cfWatson, loc. cit.Google Scholar

page 204 note 1 Proc. London Math. Soc. (2), 17 (1918), 133. It also occurs in his treatise on Bessel Functions (1922), 236.Google Scholar