Page:Philosophical Transactions - Volume 145.djvu/190

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171
mr. w.h.l. russell on the theory of definite integrals.
Hence we have
Hence

But we may effect these reductions systematically by means of the following proposition due to M. Smaasen:—

If
and
then

M. Smaasen has also proved in the same paper, that if the sums of the three series

are known, we may determine the sum of the series

by means of a double integral, but we shall not want this in what follows.

Now
consequently
Now