Document Type
Lecture
Publication Date
11-11-2010
Abstract
We present a known result of an asymptotic formula for the coefficients of the Taylor series expansion of functions under certain conditions. Our results show that knowing the location of algebraic singularities of a function can tell us a great deal about the asymptotic behavior of the coefficients of its power series. We then introduce a class of orthogonal polynomials, known as the ultraspherical or Gegenbauer polynomials (of which the Legendre polynomials are a special case), and use our results to find an asymptotic formula for these polynomials for all points in the complex plane.
Relational Format
presentation
Recommended Citation
Northington, Michael V, "An Asymptotic Formula for the Taylor Series Coefficients of Functions with Algebraic Singularites" (2010). Analysis Seminar. 15.
https://egrove.olemiss.edu/math_analysis/15
