勒让德多项式 (1-x)-P(x) 22! dx P(x)=∑(-1 2l-2k) 1-2k k=0 k2(-k)!(-2k) P(x)= 2 0 dx ()=1P(-1)=(-1yP(x)s1 1(x)P(x)x=0 2 2l+1勒让德多项式 (1 ) 2 ( 1) 0 2 2 2 + +  =  −  − l l dx d x dx d x l k l l k k l x k l k l k l k P x 2 [ / 2] 0 !2 ( )!( 2 )! (2 2 )! ( ) ( 1) − = − − − =  − l l l l l x dx d l P x ( 1) 2 ! 1 ( ) 2 = − l l l l l x dx d l P x ( 1) 2 ! 1 ( ) 2 = − P1 (1) =1 l P( 1) ( 1) 1 − = − Pl (x) 1 ( ) ( ) 0 1 1 =  − P x P x dx k l 2 1 2 2 + = l Nl