514 Higher Engineering Mathematics
term in x 5 .
⎡
⎢
⎢
⎢
⎢
⎢
⎣
(a) y = a 0 + a 1
x +
x 3
3
+
x 5
5
+ · · ·
(b) y = a 0
1 − 3x 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
35x 4 − 30x 2 + 3
(c)
1
8
63x 5 − 70x 3 + 15x
⎤
⎥
⎦
term in x 5 .
⎡
⎢
⎢
⎢
⎢
⎢
⎣
(a) y = a 0 + a 1
x +
x 3
3
+
x 5
5
+ · · ·
(b) y = a 0
1 − 3x 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
35x 4 − 30x 2 + 3
(c)
1
8
63x 5 − 70x 3 + 15x
⎤
⎥
⎦