N20 - ME 510 NUMERICAL METHODS FOR ME II ORTHOGONAL...

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ME – 510 NUMERICAL METHODS FOR ME II gG±²³´µG³´¶·G¸¹´ºG»¼½ Fall 2007 ORTHOGONAL POLYNOMIALS Name Range of Orthogonality Weighting Function Integral Property 1 k 2 2 dx P P w 1 1 - k k g G ± g Legendre [- 1 , + 1] w(x) = 1 Chebyshev [- 1 , + 1] x - 1 1 (x) w 2 G 0 k if dx T T w 1 1 - k k G ² G ± g 0 k if 2 dx T T w 1 1 - k k ³ ² G ± g Laguerre [0 , g ] w (x) = x G e -x ! k 1) k ( dx L L w 0 k k g g ´ µ G ± ´ ´ Hermite [- ¾ , + g ] e (x) w 2 x - G ! k 2 dx H H w k - k k ² G ± g ME – 510 NUMERICAL METHODS FOR ME II gG±²³´µG³´¶·G¸¹´ºG»¼½ Fall 2007 Legendre Polynomials P 0 (x) = 1 P 1 (x) = x 1) - x (3 2 1 (x) P 2 2 G x) 3 - x (5 2 1 (x) P 3 3 G 3) x 30 - x (35 8 1 (x) P 2 4 4 g G x) 15 x 70 - x (63 8 1 (x) P 3 5 5 g G Chebyshev Polynomials T 0 (x) = 1 T 1 (x) = x T 2 (x) = 2 x 2 - 1 T 3 (x) = 4 x 3 - 3 x T 4 (x) = 8 x
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N20 - ME 510 NUMERICAL METHODS FOR ME II ORTHOGONAL...

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