HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 251
Sigmavx, Sturmab
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hp40g+.book Page 69 Friday, December 9, 2005 1:03 AM SIGMAVX STURMAB Example Typing: SIGMA(X · X!, X) gives: X! because (X + 1)! - X! = X · X!. Returns the discrete antiderivative of the input function, that is a function, G, that satisfies the relation: G(x + 1) - G(x) = f(x). SIGMAVX has as its argument a function f of the current variable VX. Example Typing: SIGMAVX(X2) gives: 2----x---3---------3---x---2----+-----x6 because: 2(x + 1)3 - 3(x + 1)2 + x + 1 - 2x3 + 3x2 - x = 6x2 Returns the number of zeros of P in [a, b[ where P is a polynomial and a and b are numbers. Example 1 Typing: STURMAB(X2 · (X3 + 2), -2, 0) gives: 1 Example 2 Typing: STURMAB(X2 · (X3 + 2), -2, 1) gives: 3 Computer Algebra System (CAS) 14-69
Computer Algebra System (CAS)
14-69
Example
Typing:
SIGMA(X · X!, X)
gives:
X!
because (X + 1)! – X! = X · X!.
SIGMAVX
Returns the discrete antiderivative of the input function,
that is a function, G, that satisfies the relation: G(
x
+ 1) –
G(
x
) = f(
x
). SIGMAVX has as its argument a function
f
of
the current variable VX.
Example
Typing:
SIGMAVX(X
2
)
gives:
because:
STURMAB
Returns the number of zeros of
P
in [
a
,
b
[ where
P
is a
polynomial and
a
and
b
are numbers.
Example 1
Typing:
STURMAB(X
2
· (X
3
+ 2), –2, 0)
gives:
1
Example 2
Typing:
STURMAB(X
2
· (X
3
+ 2), –2, 1)
gives:
3
2
x
3
3
x
2
–
x
+
6
-------------------------------
2
x
1
+
(
)
3
3
x
1
+
(
)
2
–
x
1
2
x
3
–
3
x
2
x
–
+
+
+
6
x
2
=
hp40g+.book
Page 69
Friday, December 9, 2005
1:03 AM