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Numerical Evaluation of Special Functions
 In W. Gautschi (Ed.), AMS Proceedings of Symposia in Applied Mathematics 48
, 1994
"... . This document is an excerpt from the current hypertext version of an article that appeared in Walter Gautschi (ed.), Mathematics of Computation 19431993: A HalfCentury of Computational Mathematics, Proceedings of Symposia in Applied Mathematics 48, American Mathematical Society, Providence, ..."
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Cited by 21 (0 self)
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. This document is an excerpt from the current hypertext version of an article that appeared in Walter Gautschi (ed.), Mathematics of Computation 19431993: A HalfCentury of Computational Mathematics, Proceedings of Symposia in Applied Mathematics 48, American Mathematical Society, Providence, RI 02940, 1994. The symposium was held at the University of British Columbia August 913, 1993, in honor of the fiftieth anniversary of the journal Mathematics of Computation. The original abstract follows. Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field. 5.9. Mathieu, Lam'e, and Spheroidal Wave Functions. 5.9.1. Characteristic Values of Mathieu's Equation. Software Packages:...
Analytic continuation of mellin transforms up to twoloop order
 Comput. Phys. Commun
, 2000
"... The analytic continuation of the Mellin transforms to complex values of N for the basic functions gi(x) of the momentum fraction x emerging in the quantities of massless QED and QCD up to two–loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering ..."
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The analytic continuation of the Mellin transforms to complex values of N for the basic functions gi(x) of the momentum fraction x emerging in the quantities of massless QED and QCD up to two–loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space and timelike momentum transfer are evaluated. These Mellin transforms provide the analytic continuations of all finite harmonic sums up to the level of the threefold sums of transcendentality four, where the basis–set gi(x) consists of products of Nielsen–integrals up to transcendentality four. The computer code ANCONT is provided. Title of program: ANCONT Version: 1.0
THE GALOIS GROUP OF THE CHEBYSHEV POLYNOMIALS OF THE FIRST KIND OF PRIME DEGREE
"... The Galois Group of a polynomial p(x) is a group associated with p(x). It is a discrete structure arising from the algebraic Galois Theory of Equations. The Galois Group provides a connection between the algebraic theories of fields and groups. There is a close relationship between the roots of a po ..."
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The Galois Group of a polynomial p(x) is a group associated with p(x). It is a discrete structure arising from the algebraic Galois Theory of Equations. The Galois Group provides a connection between the algebraic theories of fields and groups. There is a close relationship between the roots of a polynomial and its Galois Group, to wit, the Galois Group of a polynomial refers to a certain permutation group of the roots of the polynomial. In this paper, it is shown that the Galois group of the Chebyshev polynomials of the first kind of prime degree over the field of rationals (a field of zero characteristic) is isomorphic to the cyclic group of order two. The result is established via the concept of a splitting field.