HP 40gs User Manual
Page 207
Computer Algebra System (CAS)
14-25
Typing:
gives:
•
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:
Example 2
Give a 2nd-order expansion of
in the
vicinity of x=+∞, taking as infinitely small
.
gives:
•
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.
SERIES COS 2 X
⋅
(
)
2
X
π
6
---
=
4
,
,
⎝
⎠
⎛
⎞
1
4
---
3h 2h
2
8 3
3
----------h
3
8
3
---h
4
0
h
5
4
-----
⎝ ⎠
⎛ ⎞
+
–
+
+
–
h
X
π
6
---
–
=
〈
|
〉
h
1
x
---
=
π
2
---
⎝
⎛
h
h
3
3
----- h
5
5
----- 0 π h
6
⋅
2
-------------
⎝
⎠
⎛
⎞
⎠
⎞
+
–
+
–
h
1
x
---
=
2x 1
–
(
)e
1
x
1
–
-----------
h
1
x
---
=
SERIES 2X 1
)
–
(
(
EXP
1
X 1
–
------------
⎝
⎠
⎛
⎞ X
∞
+
3)
,
=
,
⋅
12 6h 12h
2
17h
3
+
+
+
6 h
⋅
------------------------------------------------------- 0 2 h
3
⋅
(
)
+
h
1
x
---
=
hp40g+.book Page 25 Friday, December 9, 2005 1:03 AM