Page:Philosophical Transactions - Volume 145.djvu/197

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mr. w.h.l. russell on the theory of definite integrals

culation of the electrical arrangement depends upon the value of the definite integral,

I mention this on account of its analogy with the definite integral

whose value is found above. The principles contained in this paper will enable us at once to find the sums of the series

and of many others which can be imagined, by means of definite integrals. The definite integral of Poisson given above occurs in the solution of a functional equation; and it is probable that series similar to those I have been discussing in this paper, may be useful in enabling us to express the solutions of other functional equations by definite integrals.