IKBFU's Vestnik

2014 Issue №10

Back to the list Download an article

Generating function and its application for generalization of Legendre polynomials



In the present paper the generalization of Legendre polynomials with the help of generating function is studied. The explicit form of considered functions is found. Some special cases are considered. Particular attention is paid to the case when the parameters defining the studied functions are different, symmetric about zero real numbers. Some properties of constructed functions are obtained. Based on the results of numerical experiment a hypothesis about zeroes of these functions is stated.


1. Suetin P. K. Classical orthogonal polynomials. Moskow, 1978. (in Russian)
2. Dzhrbashyan M. M, Kitbalyan A. A. On one generalization of Chebyshev polynomials// Reports of Armenian SSR Academy of science. 1964. Vol. 38, N 5.P. 263—270. (in Russian)
3. Rovba E. A. Orthogonal systems of rational functions on the segment and quadratures of Gauss-type // Mathematica Balkanica. 1999. Vol. 13, N 1—2. P. 187—198.