Associated functions P0(t)=1 Pnm(t): n is called P0()=t degree; m is order P1()=-(1-t2)2 m<=n. In some P20(1)=(32-1) areas m can be P21()=-3(1-2)2 negative. In gravity P2(t)=3(1-12) formulations m=>0 http://mathworld.wolframcom/legendrepoLynomial.html 02/1302 12.540Lec0302/13/02 12.540 Lec 03 9 Associated functions • Pnm(t): n is called degree; m is order • m<=n. In some areas, m can be negative. In gravity formulations m=>0 P00 ( t ) = 1 P10 ( t ) = t P11 ( t ) = −(1 − t 2 )1/ 2 P20 ( t ) = 1 2 (3 t 2 −1) P21 ( t ) = − 3 t(1 − t 2 )1/ 2 P22 ( t ) = 3( 1 − t 2 ) http://mathworld.wolfram.com/LegendrePolynomial.html