Szilagyiova and A. (2016) The EulerGompertz Constant and its relations to Wallis' Hypergeometric Series. Master's Thesis / Essay, Mathematics.

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Abstract
Basic rules and definitions for summing divergent series, regularity, linearity and stability of a summation method. Examples of common summation methods: averaging methods, analytic continuation of a power series, Borel's summation methods. Introducing a formal totally divergent power series F(x)=0!  1!x + 2!x^2  3!x^3 + ... The main interest is the value at x=1 called Wallis' hypergeometric series (WHS). Examine the four summation methods used by Euler to assign a finite value delta ~ 0.59 (EulerGompertz constant) to this series: (1) Solving an ordinary differential equation that has a formal power series solution F(x); (2) Repeated application of Euler transform  a regular summation method useful to accelerate oscillating divergent series; (4) Extrapolating a polynomial P(n) which formally gives WHS at n=0; (3) Expanding F(x) as a continued fraction and inspecting its convergence. Multiple connections among the four methods are established, mainly by notions of asymptotic series and Borel summability. The value of delta is approximated by 3 methods, at most to a precision of several thousand decimal places.
Item Type:  Thesis (Master's Thesis / Essay) 

Degree programme:  Mathematics 
Thesis type:  Master's Thesis / Essay 
Language:  English 
Date Deposited:  15 Feb 2018 08:26 
Last Modified:  15 Feb 2018 08:26 
URI:  https://fse.studenttheses.ub.rug.nl/id/eprint/14734 
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