itself, the index of the function we are ultimately to obtain, in which case the general form would be
and
would only enter in the coefficients. Again, other functions of
or of
instead of powers, might be selected. It might be in addition proposed, that the coefficients themselves should be arranged according to given functions of a certain quantity. Another mode would be to make equations arbitrarily amongst the coefficients only, in which case the several functions, according to either of which it might be possible to develop the