Page:Scientific Memoirs, Vol. 1 (1837).djvu/470

458 the last of these quantities will satisfy the equation (4), and will be its complete integral.

If the successive substitutions are performed, and, for brevity's sake, we make which gives, in the particular case of $$\prime = i$$, $$a_i^{(0)} = \left[ 1 + \frac\right]^i$$, we shall have

Now if we make where $$\alpha$$ is put instead of $$\sqrt{ \frac}$$ we shall have and the expression for $$F$$ may take the form