Returns true if the expression f is an indexed function in the name(s) x, that is, if the input is a function and the variable(s) x are used as the index variable in a derivative, limit, integral, sum, product, and transform (for example, fourier and laplace). The purpose of this routine is to avoid substitution for x in an expression like diff(f(x), x) or int(f(x), x=a..b) where substitution of $x=y^2$ would produce an erroneous expression, for example.

$f≔\mathrm{diff}\left(g\left(x\right)\,x\right)$

$f≔\frac{\ⅆ}{\ⅆx}g\left(x\right)$

$\mathrm{type}\left(f\,\mathrm{indexedfun}\left(x\right)\right)$

$\mathrm{true}$

$\mathrm{type}\left(f\,\mathrm{indexedfun}\left(y\right)\right)$

$\mathrm{false}$

$f≔\mathrm{int}\left(g\left(t\right)\,t=1..2\right)$

$f≔{\int }_1^{2}g\left(t\right)\ⅆt$

$\mathrm{type}\left(f\,\mathrm{indexedfun}\left(t\right)\right)$

$\mathrm{true}$

$f≔\mathrm{limit}\left(1-\exp \left(-x\right)\,x=\mathrm{\infty }\right)$

$f≔1$

$\mathrm{type}\left(f\,\mathrm{indexedfun}\left(x\right)\right)$

$\mathrm{false}$