HP 40gs User Manual page 206

hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM
RISCH
N O T E :
SERIES
14-24
PREVAL is used for calculating an integral defined from a
primitive: it evaluates this primitive between the two limits
of the integral.
Typing:
2
PREVAL(X +X,2,3)
gives:
6
Primitive and defined integral
RISCH has two parameters: an expression and the name
of a variable.
RISCH returns a primitive of the first parameter with
respect to the variable specified in the second parameter.
Typing:
2
RISCH((2·X +1)·EXP(X
gives:
2
X·EXP(X +1)
If the RISCH parameter is the AND of two elements,
RISCH concerns itself only with the second element of the
AND, and adds the result to the first argument.
Limited n th-order expansion
SERIES has three arguments: an expression dependent on
a variable, an equality (the variable x = the value a to
which you want to calculate the expansion) and a whole
number (the order n of the limited expansion).
You can omit the name of the variable and the = sign
when this name is in VX).
SERIES returns the limited nth-order expansion of the
expression in the vicinity of x = a.
•
Example — Expansion in the vicinity of x=a
Give a limited 4th-order expansion of cos(2 · x)
π
-- -
x =
vicinity of .
6
For this you use the SERIES command.
2
+1),X)
2
in the
Computer Algebra System (CAS)