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
}
⎤
⎥
⎥
⎥
⎥⎥
⎦
- 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
)
⎤
⎥
⎦