HP 40gs User Manual page 251

hp40g+.book Page 69 Friday, December 9, 2005 1:03 AM
SIGMAVX
STURMAB
Computer Algebra System (CAS)
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:
2
SIGMAVX(X )
gives:
3 2
2x – 3x + x
------------------------------- -
6
because:
3 2
( ) ( )
2 x + 1 – 3 x + 1
Returns the number of zeros of P in [a, b[ where P is a
polynomial and a and b are numbers.
Example 1
Typing:
2 3
STURMAB(X · (X + 2), –2, 0)
gives:
1
Example 2
Typing:
2 3
STURMAB(X · (X + 2), –2, 1)
gives:
3
3 2
+ + x 1 2x – + 3x – x =
2
6x
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