Polynomial expansions in the Borel region
Hurt, John Tom
Master of Arts
This paper deals with the expansion of analytic functions into a series of polynomials. An explicit form for the polynomials is obtained in terms of the coefficients of a Taylor's expansion and of certain positive constants hk. Conditions on the constants hk are developed under which the series of polynomials will converge. In particular, conditions are imposed upon the such that a region can be found within which the series will converge to the function. This region is in general larger than the circle of convergence of the Taylor's series.