Higher Engineering Mathematics, Sixth Edition

514 Higher Engineering Mathematics

term inx^5.

⎡

⎢

⎢

⎢

⎢⎢

⎣

(a)y=a 0 +a 1

(

x+

x^3

3

+

x^5

5

+···

)

(b)y=a 0

{

1 − 3 x^2

}

+a 1

{

x−

2

3

x^3 −

1

5

x^5

}

⎤

⎥

⎥

⎥

⎥⎥

⎦

2. Find the following Legendre polynomials:
   (a)P 1 (x)(b)P 4 (x)(c)P 5 (x).
   ⎡
   ⎢
   ⎣

(a)x(b)

1

8

(

35 x^4 − 30 x^2 + 3

)

(c)

1

8

(

63 x^5 − 70 x^3 + 15 x

)

⎤

⎥

⎦