Gauss quadrature for analytic functions

1988 ◽  
pp. 178-192 ◽  
Author(s):  
T. J. Rivlin
Keyword(s):  
Analytic Functions ◽  
Gauss Quadrature

scholarly journals Error estimates for Gauss quadrature formulas for analytic functions

1968 ◽  
Vol 22 (101) ◽  
pp. 82-82 ◽  
Author(s):  
M. M. Chawla ◽  
M. K. Jain
Keyword(s):  
Error Estimates ◽  
Analytic Functions ◽  
Gauss Quadrature ◽  
Quadrature Formulas

scholarly journals Sharp Error Bounds for Jacobi Expansions and Gegenbauer--Gauss Quadrature of Analytic Functions

2013 ◽  
Vol 51 (3) ◽  
pp. 1443-1469 ◽  
Author(s):  
Xiaodan Zhao ◽  
Li-Lian Wang ◽  
Ziqing Xie
Keyword(s):  
Error Bounds ◽  
Analytic Functions ◽  
Gauss Quadrature ◽  
Jacobi Expansions ◽  
Sharp Error

scholarly journals Is Gauss quadrature optimal for analytic functions?

1985 ◽  
Vol 47 (1) ◽  
pp. 89-98 ◽  
Author(s):  
M. A. Kowalski ◽  
A. G. Werschulz ◽  
H. Woźniakowski
Keyword(s):  
Analytic Functions ◽  
Gauss Quadrature

scholarly journals Error estimates of Gaussian quadrature formulae with the third class of Bernstein-Szegő weights

2017 ◽  
Vol 11 (2) ◽  
pp. 451-469
Author(s):  
Aleksandar Pejcev
Keyword(s):  
Error Estimates ◽  
Error Bounds ◽  
Analytic Functions ◽  
Gaussian Quadrature ◽  
Gauss Quadrature ◽  
Weight Functions ◽  
Quadrature Formulae ◽  
The Third ◽  
Exact Degree ◽  
Gauss Quadrature Rules

For analytic functions we study the remainder terms of Gauss quadrature rules with respect to Bernstein-Szeg? weight functions w(t) = w?,?,?(t) = ?1+t/ 1-t/?(?-2?)t2+2?(?-?)t+?2+?2, t?(-1,1), where 0 < ? < ?, ??2?, ??? < ?-?, and whose denominator is an arbitrary polynomial of exact degree 2 that remains positive on [-1,1]. The subcase ?=1, ?= 2/(1+?), -1 < ? < 0 and ?=0 has been considered recently by M. M. Spalevic, Error bounds of Gaussian quadrature formulae for one class of Bernstein-Szeg? weights, Math. Comp., 82 (2013), 1037-1056.

Distributional boundary values of analytic functions and positive definite distributions

2015 ◽  
Vol 20 (2) ◽  
pp. 210-225
Author(s):  
Saulius Norvidas ◽  
Keyword(s):  
Analytic Functions ◽  
Positive Definite ◽  
Boundary Values

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY OPOOLA DIFFERENTIAL OPERATOR

2020 ◽  
Vol 9 (8) ◽  
pp. 5343-5348 ◽  
Author(s):  
T. G. Shaba ◽  
A. A. Ibrahim ◽  
M. F. Oyedotun
Keyword(s):  
Differential Operator ◽  
Analytic Functions
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