Page:Philosophical Transactions - Volume 145.djvu/178

Rh and we find from this the series

Whence we find, putting $$\mu$$ for $\frac{\mu^2x^2}{2^2}$ ,

Next consider the symbolical equation

and assume as the transformed equation

where $$1$$, $$\alpha$$, $$\beta$$ are the three cube roots of unity.

We must determine $$\mathrm{C}_1$$, $$\mathrm{C}_2$$, $$\mathrm{C}_3$$ according to the series we have to sum.

we find