A Note on the Contour Integral Representation of the Remainder Term for a Gauss–Chebyshev Quadrature Rule

1990 ◽  
Vol 27 (1) ◽  
pp. 219-224 ◽  
Author(s):  
Walter Gautschi ◽  
E. Tychopoulos ◽  
R. S. Varga
Keyword(s):  
Integral Representation ◽  
Remainder Term ◽  
Quadrature Rule ◽  
Contour Integral ◽  
Chebyshev Quadrature

scholarly journals The error bounds of Gauss-Lobatto quadratures for weights of Bernstein-Szegö type

2019 ◽  
Vol 13 (3) ◽  
pp. 733-745
Author(s):  
Rada Mutavdzic ◽  
Aleksandar Pejcev ◽  
Miodrag Spalevic
Keyword(s):  
Integral Representation ◽  
Error Bounds ◽  
Remainder Term ◽  
Contour Integral ◽  
Quadrature Formulas

In this paper, we consider the Gauss-Lobatto quadrature formulas for the Bernstein-Szeg? weights, i.e., any of the four Chebyshev weights divided by a polynomial of the form ?(t) = 1-4?/(1+?)2 t2, where t ?(-1,1) and ? ? (-1,0]. Our objective is to study the kernel in the contour integral representation of the remainder term and to locate the points on elliptic contours where the modulus of the kernel is maximal. We use this to derive the error bounds for mentioned quadrature formulas.

scholarly journals The remainder term of Gauss-Radau quadrature rule with single and double end point

2017 ◽  
Vol 102 (116) ◽  
pp. 73-83
Author(s):  
Ljubica Mihic
Keyword(s):  
Weight Function ◽  
Explicit Expression ◽  
Quadrature Formula ◽  
Remainder Term ◽  
Maximum Modulus ◽  
Quadrature Rule ◽  
Contour Integral ◽  
End Point

The remainder term of quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours for Gauss?Radau quadrature formula with the Chebyshev weight function of the second kind with double and single end point. Starting from the explicit expression of the corresponding kernel, derived by Gautschi and Li, we determine the locations on the ellipses where the maximum modulus of the kernel is attained.

scholarly journals On Appel-Type Quadrature Rules

2002 ◽  
Vol 9 (3) ◽  
pp. 405-412
Author(s):  
C. Belingeri ◽  
B. Germano
Keyword(s):  
Remainder Term ◽  
Quadrature Rule ◽  
Bernoulli Numbers ◽  
Quadrature Rules ◽  
Rule Based ◽  
Numerical Example ◽  
The Given ◽  
Derivatives Of

Abstract The Radon technique is applied in order to recover a quadrature rule based on Appel polynomials and the so called Appel numbers. The relevant formula generalizes both the Euler-MacLaurin quadrature rule and a similar rule using Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the endpoints of the considered interval. In the general case, the remainder term is expressed in terms of Appel numbers, and all derivatives appear. A numerical example is also included.

Diffraction by a perfectly conducting wedge in an anisotropic plasma

1965 ◽  
Vol 61 (3) ◽  
pp. 767-776 ◽  
Author(s):  
T. R. Faulkner
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Difference Equation ◽  
Integral Representation ◽  
Surface Waves ◽  
Uniform Magnetic Field ◽  
Anisotropic Plasma ◽  
Contour Integral ◽  
Anisotropic Dielectric

SummaryThe problem considered is the diffraction of an electromagnetic wave by a perfectly conducting wedge embedded in a plasma on which a uniform magnetic field is impressed. The plasma is assumed to behave as an anisotropic dielectric and the problem is reduced, by employing a contour integral representation for the solution, to solving a difference equation. Surface waves are found to be excited on the wedge and expressions are given for their amplitudes.

THE EIGENVECTORS OF q-DEFORMED CREATION OPERATOR $a_q^+$ AND THEIR PROPERTIES

1995 ◽  
Vol 10 (08) ◽  
pp. 669-675
Author(s):  
GUOXIN JU ◽  
JINHE TAO ◽  
ZIXIN LIU ◽  
MIAN WANG
Keyword(s):  
Integral Representation ◽  
Creation Operator ◽  
Contour Integral ◽  
Root Of Unity

The eigenvectors of q-deformed creation operator [Formula: see text] are discussed for q being real or a root of unity by using the contour integral representation of δ function. The properties for the eigenvectors are also discussed. In the case of qp = 1, the eigenvectors may be normalizable.

Contour integral representation of the on-shell T matrix

1988 ◽  
Vol 66 (9) ◽  
pp. 791-795
Author(s):  
Helmut Kröger
Keyword(s):  
Numerical Calculation ◽  
Integral Representation ◽  
Short Range ◽  
Reference Value ◽  
Potential Scattering ◽  
Contour Integral ◽  
Body System ◽  
T Matrix ◽  
Body Potential ◽  
Separable Interaction

We suggest a contour integral representation for the on-shell T matrix in nonrelativistic N-body potential scattering with strong short range interactions. Results of a numerical calculation in the two-body system using a short range separable interaction of the Yamaguchi type are presented and show fast convergence towards the reference value.

Sign in / Sign up

Export Citation Format

Share Document