On Laplace's and Gauss' summation-formulas
- 1 January 1924
- journal article
- research article
- Published by Taylor & Francis in Scandinavian Actuarial Journal
- Vol. 1924 (1) , 1-15
- https://doi.org/10.1080/03461238.1924.10405365
Abstract
In a former paper 1 On certain Formulas of Approximate Summation and Integration. The Journal of the Institute of Actuaries, vol. LIII, p. 192. Quoted below as “Approximate Summation”. View all notes I have given elementary proofs of certain formulas of summation (if the integral is known) or integration (if the sum is known), amongst them the formulas and which are ascribed, apart from their remainder-terms, to Laplace and Gauss respectively. 2 They were probably known already by Newton. View all notes Other formulas of a similar nature, both for single and repeated integration, have been derived by purely formal calculations by Gauss and have, since his time, been used extensively by astronomers for the numerical integration of differential equations; but before proceeding to examine their remainder-terms, we will stop to consider a little more closely the formulas (1) and (2).Keywords
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