These functions are used to define matrix exponentials.
One property of these functions can be calculated by taking the limit supremum of an associate
 sequence to the one over n, according to the Cauchy-Hadamard theorem. Another important property for
 them can be rewritten into Schlömilch form. These functions are used to define matrix exponentials. For
 complex holomorphic functions, these functions will always converge. Laurent names an object that
 generalizes them. Using their namesake's theorem, one can calculate an appropriate term for these items
 with a radius of convergence. An analytic function is equal to its this function at every points in an open
 interval. The exponential function can expressed in terms of these by a power divided by a factorial. For 10
 points, name these infinite sums named for an English mathematician, used to approximate functions.
One property of these functions can be calculated by taking the limit supremum of an associate
 sequence to the one over n, according to the Cauchy-Hadamard theorem.
{Taylor series} [accept {Maclaurin series} I guess; prompt on power series]