DeepAI
Log In Sign Up

Numerical Evaluation of Mittag-Leffler Functions

08/08/2022
by   William McLean, et al.
0

The Mittag-Leffler function is computed via a quadrature approximation of a contour integral representation. We compare results for parabolic and hyperbolic contours, and give special attention to evaluation on the real line. The main point of difference with respect to similar approaches from the literature is the way that poles in the integrand are handled. Rational approximation of the Mittag-Leffler function on the negative real axis is also discussed.

READ FULL TEXT
05/21/2022

Unitarity of some barycentric rational approximants

The exponential function maps the imaginary axis to the unit circle and,...
11/18/2013

Contour polygonal approximation using shortest path in networks

Contour polygonal approximation is a simplified representation of a cont...
10/10/2017

Representations and evaluation strategies for feasibly approximable functions

A famous result due to Ko and Friedman (1982) asserts that the problems ...
05/06/2020

Rational approximation of the absolute value function from measurements: a numerical study of recent methods

In this work, we propose an extensive numerical study on approximating t...
12/13/2020

Pseudospectral roaming contour integral methods for convection-diffusion equations

We generalize ideas in the recent literature and develop new ones in ord...
04/05/2018

Computing Stieltjes constants using complex integration

The Stieltjes constants γ_n are the coefficients appearing in the Lauren...
02/14/2022

Reproduction Capabilities of Penalized Hyperbolic-polynomial Splines

This paper investigates two important analytical properties of hyperboli...