type/indexedfun - Maple Programming Help

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type/indexedfun

for use with substitution

 Calling Sequence type(f, indexedfun(x))

Parameters

 f - expression or list or set of expressions x - name or list or set of names

Description

 • 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.

Examples

 > $f≔\frac{ⅆ}{ⅆx}g\left(x\right)$
 ${f}{:=}\frac{{ⅆ}}{{ⅆ}{x}}{}{g}{}\left({x}\right)$ (1)
 > $\mathrm{type}\left(f,\mathrm{indexedfun}\left(x\right)\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{type}\left(f,\mathrm{indexedfun}\left(y\right)\right)$
 ${\mathrm{false}}$ (3)
 > $f≔{∫}_{1}^{2}g\left(t\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}ⅆt$
 ${f}{:=}{{∫}}_{{1}}^{{2}}{g}{}\left({t}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{t}$ (4)
 > $\mathrm{type}\left(f,\mathrm{indexedfun}\left(t\right)\right)$
 ${\mathrm{true}}$ (5)
 > $f≔\underset{x→\mathrm{∞}}{lim}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\left(1-{ⅇ}^{-x}\right)$
 ${f}{:=}{1}$ (6)
 > $\mathrm{type}\left(f,\mathrm{indexedfun}\left(x\right)\right)$
 ${\mathrm{false}}$ (7)