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Functions and commands 327
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. With the
optional second and third arguments you can specify the limit
point and the order of the expansion. If no limit point is
provided, it is taken as x=0. If no order is provided, the series
returned is fifth order.
taylor(Expr,[Var=limit_point],[Order])
Example:
taylor(sin(x)/x,x,0) gives 1+x^2/-6+x^4/
120+x^6*order_size(x)
Taylor of Quotient Returns the quotient Q of the division of polynomial A by
polynomial B by increasing power order, with degree(Q)≤ n
or Q=0. In other words, Q is the Taylor expansion at order n
of A/B in the vicinity of x=0.
divpc(A,B,Intg(n))
Example:
divpc(x^4+x+2,x^2+1,5) gives 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)