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Dissertation
The Zero Attractor of Perturbed Chebyshev Polynomials and Sums of Taylor Polynomials
Doctor of Philosophy (Ph.D.), Drexel University
Sep 2019
DOI:
https://doi.org/10.17918/00000218
Abstract
Defining s_n(z) to be the nth degree Taylor polynomial at 0 for the exponential function, we employ methods from complex analysis to study the limiting behavior of the zero distribution of polynomials in the sequence As_[an]([alpha]nz) + Bs_[bn]([beta]nz) as n [right arrow] [infinity]. Invariably the zero distribution approaches one or more fixed piecewise smooth curves in the complex plane which we call the "zero attractor'' of the sequence. Also we determine the zero attractor of the sequence T_n(z) - z^[ℓn] for fixed integer ℓ [greater than or equal to] 2 and nth degree Chebyshev polynomial of the first kind T_n(z).
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Details
- Title
- The Zero Attractor of Perturbed Chebyshev Polynomials and Sums of Taylor Polynomials
- Creators
- Joseph Erickson
- Contributors
- Robert Paul Boyer (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- vii, 124 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 991014695544904721