LEGENDRE POLYNOMIAL EXPANSIONS Expansion of a ...
Legendre_expansions.nb
1
Physics 421 Prof. R. Sorbello
LEGENDRE POLYNOMIAL EXPANSIONS Expansion of a function of x on the interval –1 x 1: Consider a function F(x) defined on the interval -1 x 1. Assuming that the function is finite on this interval, it can be expanded in a series of Legendre Polynomials as follows: ‚ cL PL HxL ¶
L=0
where the coefficients are given by 1 2L+1 cL = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ‡ PL HxL F HxL „ x 2 -1
We write the expression for the expansion coefficients in Mathematica input-notation: c@L_D := HH2 L + 1L ê 2L Integrate@ LegendreP@L, xD F@xD, 8x, -1, 1
1
Physics 421 Prof. R. Sorbello
LEGENDRE POLYNOMIAL EXPANSIONS Expansion of a function of x on the interval –1 x 1: Consider a function F(x) defined on the interval -1 x 1. Assuming that the function is finite on this interval, it can be expanded in a series of Legendre Polynomials as follows: ‚ cL PL HxL ¶
L=0
where the coefficients are given by 1 2L+1 cL = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ‡ PL HxL F HxL „ x 2 -1
We write the expression for the expansion coefficients in Mathematica input-notation: c@L_D := HH2 L + 1L ê 2L Integrate@ LegendreP@L, xD F@xD, 8x, -1, 1
