Maxima Function
changevar (expr, f(x,y), y, x)
Makes the change of variable given by
f(x,y) = 0
in all integrals occurring in expr with integration with
respect to x.
The new variable is y.
(%i1) assume(a > 0)$ (%i2) 'integrate (%e**sqrt(a*y), y, 0, 4); 4 / [ sqrt(a) sqrt(y) (%o2) I %e dy ] / 0 (%i3) changevar (%, y-z^2/a, z, y); 0 / [ abs(z) 2 I z %e dz ] / - 2 sqrt(a) (%o3) - ---------------------------- a
An expression containing a noun form, such as the instances of 'integrate
above,
may be evaluated by ev
with the nouns
flag.
For example, the expression returned by changevar
above may be evaluated
by ev (%o3, nouns)
.
changevar
may also be used to changes in the indices of a sum or
product. However, it must be realized that when a change is made in a
sum or product, this change must be a shift, i.e., i = j+ ...
, not a
higher degree function. E.g.,
(%i4) sum (a[i]*x^(i-2), i, 0, inf); inf ==== \ i - 2 (%o4) > a x / i ==== i = 0 (%i5) changevar (%, i-2-n, n, i); inf ==== \ n (%o5) > a x / n + 2 ==== n = - 2