Vol.4, No 16, 2004 pp. 121-132
UDC 519.145.4(045)
ON GENERALIZATION OF MULTIVARIABLE
HARMONIC POLYNOMIALS
Lazar N. Djordjević1, Djordje Djordjević2,
Valentina M. Milićević1
1Department of Computer Sciences, Faculty
of Electronic Engineering
2Department of Mathematics and Informatics,
Faculty of Civil Engineering and Architecture, University of Niš, Serbia
& Montenegro
Abstract. In this paper is presented a class of multivariable homogeneous
orthogonal polynomials, obtained as linear combination of classical generalized
Laguerre polynomials. Using them, the generalized harmonic polynomials
are defined. It is proven that multivariable harmonic polynomials are particular
case of generalized harmonic polynomials.
Key words: Multivariable harmonic polynomials, Multivariable
hypergeometric polinomials, Gauss hypergeometric polynomials, Lauricella
functions; Laguerre polynomials, Multivariable Appell polynomials;
Jacobi shifting polynomials.
O GENERALIZACIJI HARMONIČNIH
POLINOMA
VIŠE PROMENLJIVIH
U ovom radu je predstavljena jedna klasa homogenih ortogonalnih polinoma
više promenljivih koja se dobija kao linearna kombinacija klasičnih generalisanih
Laguerreovih polinoma. Pomoću njih su definisani generalisani harmonični
polinomi. Dokazano je da su harmonični polinomi više promenljivih partikularni
slučajevi generalisanih harmoničnih polinoma.
