TY  - JOUR
AU  - Milovanović, Gradimir V.
AU  - Pranić, Miroslav S.
AU  - Spalević, Miodrag
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3083
AB  - The paper deals with new contributions to the theory of the Gauss quadrature formulas with multiple nodes that are published after 2001, including numerical construction, error analysis and applications. The first part was published in Numerical analysis 2000, Vol. V, Quadrature and orthogonal polynomials (W. Gautschi, F. Marcellan, and L. Reichel, eds.) [J. Comput. Appl. Math. 127 (2001), no. 1-2, 267-286].
PB  - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
T2  - Applicable Analysis and Discrete Mathematics
T1  - Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii
EP  - 27
IS  - 1
SP  - 1
VL  - 13
DO  - 10.2298/AADM180730018M
ER  - 

@article{
author = "Milovanović, Gradimir V. and Pranić, Miroslav S. and Spalević, Miodrag",
year = "2019",
abstract = "The paper deals with new contributions to the theory of the Gauss quadrature formulas with multiple nodes that are published after 2001, including numerical construction, error analysis and applications. The first part was published in Numerical analysis 2000, Vol. V, Quadrature and orthogonal polynomials (W. Gautschi, F. Marcellan, and L. Reichel, eds.) [J. Comput. Appl. Math. 127 (2001), no. 1-2, 267-286].",
publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd",
journal = "Applicable Analysis and Discrete Mathematics",
title = "Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii",
pages = "27-1",
number = "1",
volume = "13",
doi = "10.2298/AADM180730018M"
}

Milovanović, G. V., Pranić, M. S.,& Spalević, M.. (2019). Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii. in Applicable Analysis and Discrete Mathematics
Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 13(1), 1-27.
https://doi.org/10.2298/AADM180730018M

Milovanović GV, Pranić MS, Spalević M. Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii. in Applicable Analysis and Discrete Mathematics. 2019;13(1):1-27.
doi:10.2298/AADM180730018M .

Milovanović, Gradimir V., Pranić, Miroslav S., Spalević, Miodrag, "Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii" in Applicable Analysis and Discrete Mathematics, 13, no. 1 (2019):1-27,
https://doi.org/10.2298/AADM180730018M . .

TY  - JOUR
AU  - Cvetković, Aleksandar
AU  - Milovanović, Gradimir V.
AU  - Vasović, Nevena
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2940
AB  - Given real number s > -1/2 and the second degree monic Chebyshev polynomial of the first kind (T) over cap (2)(x), we consider the polynomial system {p(k)(2,s)} "induced" by the modified measure d sigma(2,s) (x) = vertical bar(T) over cap (2)(x)vertical bar(2s) d sigma(x) = 1/root 1 - x(2) dx is the Chebyshev measure of the first kind. We determine the coefficients of the three-term recurrence relation for the polynomials p(k)(2,s) (x) in an analytic form and derive a differential equality, as well as the differential equation for these orthogonal polynomials. Assuming a logarithmic potential, we also give an electrostatic interpretation of the zeros of p(4 nu)(2,s) (x)(nu is an element of N).
PB  - SPRINGER Basel AG, Basel
T2  - Results in Mathematics
T1  - Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials
IS  - 1
VL  - 73
DO  - 10.1007/s00025-018-0779-8
ER  - 

@article{
author = "Cvetković, Aleksandar and Milovanović, Gradimir V. and Vasović, Nevena",
year = "2018",
abstract = "Given real number s > -1/2 and the second degree monic Chebyshev polynomial of the first kind (T) over cap (2)(x), we consider the polynomial system {p(k)(2,s)} "induced" by the modified measure d sigma(2,s) (x) = vertical bar(T) over cap (2)(x)vertical bar(2s) d sigma(x) = 1/root 1 - x(2) dx is the Chebyshev measure of the first kind. We determine the coefficients of the three-term recurrence relation for the polynomials p(k)(2,s) (x) in an analytic form and derive a differential equality, as well as the differential equation for these orthogonal polynomials. Assuming a logarithmic potential, we also give an electrostatic interpretation of the zeros of p(4 nu)(2,s) (x)(nu is an element of N).",
publisher = "SPRINGER Basel AG, Basel",
journal = "Results in Mathematics",
title = "Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials",
number = "1",
volume = "73",
doi = "10.1007/s00025-018-0779-8"
}

Cvetković, A., Milovanović, G. V.,& Vasović, N.. (2018). Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials. in Results in Mathematics
SPRINGER Basel AG, Basel., 73(1).
https://doi.org/10.1007/s00025-018-0779-8

Cvetković A, Milovanović GV, Vasović N. Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials. in Results in Mathematics. 2018;73(1).
doi:10.1007/s00025-018-0779-8 .

Cvetković, Aleksandar, Milovanović, Gradimir V., Vasović, Nevena, "Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials" in Results in Mathematics, 73, no. 1 (2018),
https://doi.org/10.1007/s00025-018-0779-8 . .