Manual

Functions and commands 329
F(b)–F(a) Returns F(b)–F(a).
preval(Expr(F(var)),Real(a),Real(b),[Var])
Example:
preval(x^2-2,2,3) gives 5
Limits
Riemann Sum Returns in the neighborhood of n=+∞ an equivalent of the
sum of Xpr(var1,var2) for var2 from var2=1 to var2=var1
when the sum is looked at as a Riemann sum associated with
a continuous function defined on [0,1].
sum_riemann(Expr(Xpr),Lst(var1,var2))
Example:
sum_riemann(1/(n+k),[n,k]) gives ln(2)
Taylor Returns the Taylor series expansion of an expression at a point
or at infinity (by default, at x=0 and with relative order=5).
taylor(Expr,[Var=Value],[Order])
Example:
taylor(sin(x)/x,x=0) returns 1-(1/6)*x^2+(1/
120)*x^4+x^6*order_size(x)
Taylor of Quotient Returns the n-degree Taylor polynomial for the quotient of 2
polynomials.
divpc(Poly1,Poly2,Integer)
Example:
d divpc(x^4+x+2,x^2+1,5) returns the 5th-degree
polynomial
x^5+3*x^4-x^3-2*x^2+x+2
Transform
Laplace Returns the Laplace transform of an expression.
laplace(Expr,[Var],[LapVar])
Example:
laplace(exp(x)*sin(x)) gives 1/(x^2-2*x+2)