Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials

Marčoková, Mariana; Guldan, Vladimír

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 287-294

Abstract

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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.

How to cite

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Marčoková, Mariana, and Guldan, Vladimír. "Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 287-294. <http://eudml.org/doc/294899>.

@inProceedings{Marčoková2017,
abstract = {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.},
author = {Marčoková, Mariana, Guldan, Vladimír},
booktitle = {Proceedings of Equadiff 14},
keywords = {Orthogonal polynomial, weight function, classical Jacobi polynomial, classical Legendre polynomial, generalized orthogonal polynomial, differential equation},
location = {Bratislava},
pages = {287-294},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials},
url = {http://eudml.org/doc/294899},
year = {2017},
}

TY - CLSWK
AU - Marčoková, Mariana
AU - Guldan, Vladimír
TI - Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 287
EP - 294
AB - 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.
KW - Orthogonal polynomial, weight function, classical Jacobi polynomial, classical Legendre polynomial, generalized orthogonal polynomial, differential equation
UR - http://eudml.org/doc/294899
ER -

References

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  1. Andrews, L. C., Special Functions of Mathematics for Engineers, , Second ed., McGraw-Hill, Inc., 1992. MR1254207
  2. Hofman-Wellenhof, B., Moritz, H., Physical Geodesy, , Second ed., Springer, 2006. 
  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. 
  4. Korous, J., Special Parts of Mathematics, . Orthogonal Functions and Orthogonal Polynomials, SNTL, Prague, 1958 (in Czech). 
  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. MR2442392
  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. 
  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. MR2323584
  8. Sujetin, P. K., Classical orthogonal polynomials, , Nauka, Moskva, 1979 (in Russian). MR0548727
  9. Szegö, G., Orthogonal polynomials, , Nauka, Moskva, 1969 (in Russian). MR0000077
  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. 
  11. Tenzer, R., Methodology for testing of geopotential model, , Studies of University in Žilina, Civil Engineering series, 25 (2002), 113–116. 

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