"2nd. We first perceive that this expression contains an infinite number of terms, into which unknown constants enter, or that it is equal to an which includes one or more arbitrary functions. In the first instance, [i.e.], when the general term is affected by the symbol \textstyle \sum , we derive from the special conditions a definite , whose roots give the values of an infinite number of constants. The second instance... when the general term becomes... infinitely small... the sum of the series is... changed into a definite integral."
January 1, 1970
https://en.wikiquote.org/wiki/The_Analytic_Theory_of_Heat