Josip Juraj Strossmayer University of Osijek. Department of Physics. The Division of Experimental and Theoretical Physics. Division Chair of Theoretical Computational Physics.
Abstract
Legendreovi polinomi rješenja su Legendreove diferencijalne jednadžbe
\left(1-x^{2}\right)P^{n}-2xP^{'}\left(x\right)+\lambda P\left(x\right)=0.
Pomoću ove diferencijalne jednadžbe također se može dobiti funkcija izvodnica.
Nadalje, ona će nam pomoći u izračunu rekurzivnih relacija. Legendreovi polinomi
imaju široku primjenu u mnogim granama fizike. Nalazimo ih u elektrodinamici te u kvantoj
mehanici.Legendre polynomials are solution to Legendre differential equation \left(1-x^{2}\right)P^{n}-2xP^{'}\left(x\right)+\lambda P\left(x\right)=0.From Legendre differential equation we can calculate generating function.
Further, from generating function we can calculate recurrence formulas. Legendre polynomials
are widely used in many branches of physics. They are used in electrodynamics as well as in
quantum physics
