The elementary functions are denoted by (1), (12), (13), ...

00The sum of the monomial functions of a given weight is called the homogeneous-product-sum or complete symmetric function of that weight; it is denoted by h.; it is connected with the elementary functions by the formula 1 7r1l7r2!7r3!

00by the same law which expresses the power function s, in terms of the elementary functions a 1, a2, a3,...

00The partitions with one bipart correspond to the sums of powers in the single system or unipartite theory; they are readily expressed in terms of the elementary functions.

00in terms of elementary functions can be at once written down.

00which expresses the elementary functions in terms of the single bipart functions.

00This paper offers a glimpse of how Euler used infinitesimals and infinite series to compute differentials for the elementary functions.

00The result of this is that the provably recursive functions of the theory are now exactly the Kalmar Elementary functions.

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