Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials
Само за регистроване кориснике
2018
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
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).
Кључне речи:
recurrence relation / Orthogonal polynomials / differential equation / Chebyshev polynomials / Chebyshev measureИзвор:
Results in Mathematics, 2018, 73, 1Издавач:
- SPRINGER Basel AG, Basel
Финансирање / пројекти:
- Апроксимација интегралних и диференцијалних оператора и примене (RS-MESTD-Basic Research (BR or ON)-174015)
- Serbian Academy of Sciences and Arts [Phi-96]
DOI: 10.1007/s00025-018-0779-8
ISSN: 1422-6383
WoS: 000426765600031
Scopus: 2-s2.0-85041401572
Колекције
Институција/група
Mašinski fakultetTY - 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 . .