Pade' approximations to the exponential function
Abstract
This dissertation contains a Pade' approximation for the
exponential function. The Pade' approximation happens to be a
rational approximation that is unique and is in fact a generalisation
of the truncated Taylor services expansion. It converges
much faster than the Taylor series and is very useful among
other things in the numerical inversion of Laplace transforms by
use of Bromwich's integral.
A general definition of the Pade' approximation is given
then a Pade' approximation to the exponential function is derived.
An analysis of the Pade' approximant and the polynomials forming
the approximant is given and finally some analysis of a hypergeometic
function containing indeterminate terms is given.
This confluent hypergeometic function is part of thePade'
approximation for the exponential function.
The variables and parameters used in this paper are to
be considered complex unless its specifically stipulated that
they are real, but the parameters m and n of the Pade'
approximant for the exponential function will be assumed to be
positive integers even if it is not stated.
Citation
Master of Science, University of Nairobi, 1981Publisher
University of Nairobi, Department of Mathematics