| Title:
|
Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials (English) |
| Author:
|
Marčoková, Mariana |
| Author:
|
Guldan, Vladimír |
| Language:
|
English |
| Journal:
|
Proceedings of Equadiff 14 |
| Volume:
|
Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017 |
| Issue:
|
2017 |
| Year:
|
|
| Pages:
|
287-294 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this contribution we deal with classical Jacobi polynomials orthogonal with respect to different weight functions, their special cases - classical Legendre polynomials and generalized brothers of them. We derive expressions of generalized Legendre polynomials and generalized ultraspherical polynomials by means of classical Jacobi polynomials. (English) |
| Keyword:
|
Orthogonal polynomial, weight function, classical Jacobi polynomial, classical Legendre polynomial, generalized orthogonal polynomial, differential equation |
| MSC:
|
33C45 |
| MSC:
|
42C05 |
| . |
| Date available:
|
2019-09-27T08:13:18Z |
| Last updated:
|
2019-09-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703029 |
| . |
| Reference:
|
[1] Andrews, L. C.: Special Functions of Mathematics for Engineers., Second ed., McGraw-Hill, Inc., 1992. MR 1254207 |
| Reference:
|
[2] Hofman-Wellenhof, B., Moritz, H.: Physical Geodesy., Second ed., Springer, 2006. |
| Reference:
|
[3] Janecki, D., Stepien, K.: Legendre polynomials used for the approximation of cylindrical surfaces., Communications - Scientific Letters of the University of Žilina, 4 (2005), 59–61. |
| Reference:
|
[4] Korous, J.: Special Parts of Mathematics.. Orthogonal Functions and Orthogonal Polynomials, SNTL, Prague, 1958 (in Czech). |
| Reference:
|
[5] Livermore, P. W., Jones, CH. A., HASH(0x2637898), Worland, S. J.: Spectral radial basis functions for full sphere computations., J. Comput. Phys., 227 (2007), 1209–1224. MR 2442392, 10.1016/j.jcp.2007.08.026 |
| Reference:
|
[6] Marčoková, M., Guldan, V.: Jacobi Polynomials and Some Related Functions., in Mathematical Methods in Engineering, N. M. F. Ferreira and J. A. T. Machado, eds., Springer, 2014, pp. 219–227. |
| Reference:
|
[7] Mirevski, S. P., Boyadijev, L., HASH(0x263aa58), Scherer, R.: On the Riemann-Liouville fractional calculus, g-Jacobi functions and F-Gauss functions., Appl. Math. Comput., 187(1) (2007), 315–325. MR 2323584 |
| Reference:
|
[8] Sujetin, P. K.: Classical orthogonal polynomials., Nauka, Moskva, 1979 (in Russian). MR 0548727 |
| Reference:
|
[9] Szeg\"o, G.: Orthogonal polynomials., Nauka, Moskva, 1969 (in Russian). MR 0000077 |
| Reference:
|
[10] Tenzer, R.: Geopotential model of Earth - approximation of Earth shape, geopotential model testing methods., Communications - Scientific Letters of the University of Žilina, 4 (2001), 50–58. |
| Reference:
|
[11] Tenzer, R.: Methodology for testing of geopotential model., Studies of University in Žilina, Civil Engineering series, 25 (2002), 113–116. |
| . |
