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The summation of a slowly convergent series

Published online by Cambridge University Press:  31 October 2008

S. Paterson
S. Paterson
Affiliation:
Gairview, Glencairn St., Stevenston, Ayrshire.
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The series

in which r is zero or an integer is rapidly convergent if x is large but may be very slowly convergent if x is small. The object of this note is to derive an alternative series for S2r(x) which is rapidly convergent for small values of x.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 38 , January 1952 , pp. 5 - 7
Copyright
Copyright © Edinburgh Mathematical Society 1952

References

1 Hartree, D. R., Mem. Proc. Manchester Lit. Phil. Soc., 38, 85, (1936).Google Scholar