scholarly journals Addendum to: “Rational approximation ofe−xon the positive real axis”

1977 ◽  
Vol 68 (2) ◽  
pp. 489-489
Author(s):  
Donald Newman ◽  
A. Reddy
Keyword(s):  
Real Axis ◽  
Rational Approximation ◽  
Positive Real Axis ◽  
Positive Real

On Rational Approximation on the Positive Real Axis

1977 ◽  
Vol 29 (1) ◽  
pp. 180-192 ◽  
Author(s):  
Q. I. Rahman ◽  
G. Schmeisser
Keyword(s):  
Real Axis ◽  
Rational Approximation ◽  
Uniform Approximation ◽  
Positive Real Axis ◽  
Positive Real ◽  
Image Position

In their study of the uniform approximation of the reciprocal of e2 by reciprocals of polynomials on the positive real axis, Cody, Meinardus, and Varga [3] showed that if denotes the class of all polynomials of degree at most n andthen

scholarly journals An Extension of the Almost Isolated Singularity of Finite Exponential Order

1964 ◽  
Vol 14 (2) ◽  
pp. 137-141
Author(s):  
R. Wilson
Keyword(s):  
Real Axis ◽  
Taylor Series ◽  
Positive Real Axis ◽  
Isolated Singularity ◽  
Positive Real ◽  
Small Disk ◽  
Exponential Order ◽  
Disk Centre ◽  
Image Position

Let f(z) be represented on its circle of convergence |z| = 1 by the Taylor seriesand suppose that its sole singularity on |z| = 1 is an almost isolated singularity at z = 1. In the neighbourhood of such a singularity f(z) is regular on a sufficiently small disk, centre z = 1, with the outward drawn radius along the positive real axis excised. If also in this neighbourhood |f(z)| e−(1/δ)ρ remains bounded for some finite ρ, where δ is the distance from the excised radius, then the singularity is said to be of finite exponential order.

scholarly journals Integral representations of Mittag-Leffler function on the positive real axis

2019 ◽  
Vol 20 (2) ◽  
pp. 217
Author(s):  
Eliana Contharteze Grigoletto ◽  
Edmundo Capelas Oliveira ◽  
Rubens Figueiredo Camargo
Keyword(s):  
Fractional Calculus ◽  
Laplace Transform ◽  
Real Axis ◽  
Integral Representations ◽  
Positive Real Axis ◽  
Inverse Laplace Transform ◽  
Positive Real

The Mittag-Leffler functions appear in many problems associated with fractional calculus. In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N. Berberan-Santos, to show that the three-parameter Mittag-Leffler function has similar integral representations on the positive real axis. Some of the integrals are also presented.

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