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A General Method of Obtaining the Finite Integral of any Rational Algebraic Function of x: or Summing any Series of which such a Function is the General Term

Published online by Cambridge University Press:  18 August 2016

William Orchard
William Orchard*
Affiliation:
Fellow of the Institute of Actuaries
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Extract

Let be the given function, then, by a well known theorem

the integral of which, since u 0, δu 0, δ2 u 0, &c., are constants, and

will be

which differs from (A) only by the coefficients of δu 0, δ2 u 0, &c, being shifted each one place to the left.

Information

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 1 , Issue 2 , 1851 , pp. 9 - 11
Copyright
Copyright © Institute and Faculty of Actuaries 1851

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