Page:Philosophical Transactions - Volume 145.djvu/178

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159
MR. W.H.L. RUSSELL ON THE THEORY OF DEFINITE INTEGRALS.

and we find from this the series

Whence we find, putting for ,

Next consider the symbolical equation

, where ;

and assume as the transformed equation

.

Then
and

where , , are the three cube roots of unity.

Hence


We must determine , , according to the series we have to sum.

If

we find

Whence