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
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
(%o1) true (%i2)