th function. We suppose him likewise to comprehend distinctly the difference between developing an
th function algebraically, and merely calculating an
th function arithmetically. If he does not, the following will be by no means very intelligible; but we have not space to give any preliminary explanations. To proceed: the law, according to which the successive functions of (5.) are to be developed, must of course first be fixed on. This law may be of very various kinds. We may propose to obtain our results in successive powers of
, in which case the general form would be
or in successive powers of