HP 40gs User Manual page 207

Computer Algebra System (CAS)
Typing:
⎛
(
SERIES COS 2 X
⎝
gives:
1
2
〈
-- -
– 3h + 2h
4
• Example — Expansion in the vicinity of x=+∞
or x=–∞
Example 1
Give a 5th-order expansion of arctan(x) in the vicinity of
x=+∞, taking as infinitely small
Typing:
SERIES(ATAN(X),X =+∞,5)
gives:
3
π
h ---- - h
⎛
-- - ---- -
– h + –
⎝
2 3 5
Example 2
Give a 2nd-order expansion of
vicinity of x=+∞, taking as infinitely small
SERIES 2X 1 ) ( (
–
gives:
2
12 + 6h + 12h
------------------------------------------------------ -
6 h ⋅
•
Unidirectional expansion
To perform an expansion in the vicinity of x = a where
x > a, use a positive real (such as 4.0) for the order.
To perform an expansion in the vicinity of x = a where
x < a, use a negative real (such as –4.0) for the order.
π
⎞
2
⋅ ) , ,
-- -
X = 4
⎠
6
8 3 8
3 4
--------- - h -- - h
+ – + 0
3 3
h =
5 6
π h ⋅
⎛ ⎞ ⎞
------------ -
+ 0
⎝ ⎠ ⎠
2 h =
(
2x 1
1
⎛ ⎞ X
⋅
----------- -
EXP ,
⎝ ⎠
X 1 –
3
+ 17h
3
( ⋅ )
+ 0 2 h
5
h
⎛ ⎞
π
| 〉
---- -
⎝ ⎠ -- -
h = X –
4
6
1
-- -
.
x
1
-- -
x
1
---------- -
x 1 –
)e
–
in the
1
-- -
h =
.
x
∞
= + , 3)
1
-- -
h =
x
14-25