The exponential series that was the drive was a remarkable thing.

Bernoulli also studied the exponential series which came out of examining compound interest.

He is known for having calculated the solution to a chessboard problem involving an exponential series.

The Bernoulli numbers appear in the book in a discussion of the exponential series.

Consider, for example, the exponential series and two expressions of it that are valid when x is small:

To differentiate the associated exponential series, the sequence of coefficients needs to be shifted one place to the "left" (losing the first term).

Estimation of sinusoidal and exponential series models from short-duration nonuniformly spaced samples.

The exponential series, i.e. tending toward infinity, was discovered by Newton and is contained within the Analysis.

From these representations, you should notice that the terms of the sine and cosine series combine, along with some sign changes, to make the exponential series.

The above identities use the number "i" to remove the alternating factor ( 1) from terms of the series to restore the full halves of the exponential series.

As a freshman, he developed a generalized solution regarding Cauchy exponential series, which he published in the proceedings of the French Academy of Sciences-1935.

A Comparison of the Maximum Entropy and Exponential Series Methods for Recovery of Distributions of Lifetimes from Fluorescence Decay Data.

It might appear that this is the non-constructive equivalent of the constructive definition using iterated exponentiation; but the two definitions are equally non-constructive at steps indexed by limit ordinals, which represent transfinite recursion of a higher order than taking the supremum of an exponential series.