ESCUELA DE INGENIEROS MILITARESG
TECNOLOGÍA EN TOPOGRAFÍA

GEODESIA

EJERCICIO DE LEGENDRE

ING. MIGUEL AVILA

CS CUELLAR VALERO ADRIAN
COD.316301010

BOGOTÁ DC, 10 DE AGOSTO DE 2010
EJERCICIOS DE 6 AL 10 DE LEGENDRE

EJERCICIO # 6
P_(n ) =∑_(k=0)^n▒= ((-1)^(k ) (2*n-2*k)!)/(2^n*0!(n-k)!*(n-2*k)!) I^(n-2*k )

P6 n = 6
N = 6/2 =3

P6 ∑_(k=n)^1▒ ((〖-1)〗^0 (2*6-2*0)!)/(2^6*0!(6-0)!(6-2*0)!) τ^(6-2*0 )+ ((〖-1)〗^1 (2*6-2*1)!)/(2^6*1!(6-1)!(6-2*1)!) τ^(6-2*1 )

+ ((〖-1)〗^2 (2*6-2*2)!)/(2^6*2!(6-2)!(6-2*2)!) τ^(6-2*2 )+ ((〖-1)〗^3 (2*6-2*3)!)/(2^6*3!(6-3)!(6-2*3)!) τ^(6-2*3 )

P6 = (1*12!)/(64*1*6!*6!) τ^(6 ) - 10!/(64*1*5!*4!) τ^(4 ) + (1*8!)/(64*2*4!*2!) τ^(2 ) - 6!/(64*6*3!*1) τ^(0 )

P6 = 231/16 τ^(6 …ver más…

)/(2^n k! (n-k)!(n-2*k)!) τ^(n-2*k)

P8=∑_(K=0)^4 ((-1)^(0 ) (2*8-2*0)! )/(2^8 0! (8-0)!(8-2*0)!) τ^(8-2*0)+((-1)^(1 ) (2*8-2*1)! )/(2^8 1! (8-1)!(8-2*1)!) τ^(8-2*1)+ (〖(-1)〗^(2 ) (2*8-2*2)! )/(2^8 2! (8-2)!(8-2*2)!) τ^(8-2*2)+(〖(-1)〗^(3 ) (2*8-2*3)! )/(2^8 3! (8-3)!(8-2*3)!) τ^(8-2*3)+(〖(-1)〗^(4 ) (2*8-2*4)! )/(2^8 4! (8-4)!(8-2*4)!) τ^(8-2*4)

P8=(1* 16! )/(256*1* 8!*8!) τ^8-(1* 14! )/(256* 1* 7!*6!) τ^6+(1*12! )/(256* 2!*6!*4!) τ^4-(1* 10! )/(256* 3!* 5!*2!) τ^2+(1 *8! )/(256 *4!*4!0!) τ^0

P8=(1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16 )/(256*1*2*3*4*5*6*7*8*1*2*3*4*5*6*7*8) τ^8

-(1*2*3*4*5*6*7*8*9*10*11*12*13*14 )/(256* 1*2*3*4*5*6*7*1*2*3*4*5*6) τ^6

+(1*2*3*4*5*6*7*8*9*10*11*12 )/(256* 1*2*1*2*3*4*5*6*1*2*3*4) τ^4

-(1*2*3*4*5*6*7*8*9*10 )/(256* 1*2*3* 1*2*3*4*5*1*2) τ^2+(1*2*3*4*5*6*7*8 )/(256 *1*2*3*4*1*2*3*4)

P8=(77220 )/1536 τ^8-24024/256 τ^6+( 3860)/256 τ^4-(2520 )/256