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Formulae

# Formulae - Formulae Vsph(r = l=0 Al rl Bl rl 1 Pl(cos Vcyl...

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Formulae V sph ( r, θ, φ ) = X l =0 A l r l + B l r l +1 P l (cos θ ) V cyl ( ρ, φ ) = ( a 0 + b 0 log ρ ) ( c 0 + d 0 φ ) + X n =1 ( a n ρ n + b n ρ - n ) ( c n cos( ) + d n sin( )) ( E 2 - E 1 ) · ˆ n 1 2 = σ ² 0 ; ( E 2 - E 1 ) × ˆ n 1 2 = 0 ; cos( a + b ) = cos a cos b - sin a sin b Z a 0 sin mπx a · sin nπx a dx = a 2 δ mn ; Z a 0 cos mπx a · cos nπx a dx = a 2 δ mn ; Z a 0 cos mπx a · sin nπx a dx = 0 . P 0 ( x ) = 1 , P 1 ( x ) = x , P 2 ( x ) = (3 x 2 - 1) 2 , P 3 ( x ) = (5 x 3 - 3 x ) 2 ; P l (1) = 1 ; P l ( - 1) = ( - 1) l Z 1 - 1 dx P m ( x ) P n ( x ) = 2 2 m + 1 δ mn (1 + x ) β = 1 + β x + β ( β - 1) 2! x 2 + β ( β - 1)( β - 2)
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