Function Repository Resource:

RightComposeIndexedList

Nest an indexed list of functions to apply to an argument

Contributed by: Wolfram Staff

ResourceFunction["RightComposeIndexedList"][{f₁,f₂,f₃,…},x,{i,j,k,…}]

gives {x,f_i[x],f_j[f_i[x]],f_k[f_j[f_i[x]]],…}.

Details

ResourceFunction["RightComposeIndexedList"][flist,x,ilist] gives a list of length Length[ilist]+1.

Construct iterates from composing with a list of three functions:

In[1]:=

Out[1]=

Use a list of pure functions:

In[2]:=

$ResourceFunction[ "RightComposeIndexedList"][{#^2 + 1 &, 1 - # &, Sqrt[#] &}, 2., {3, 2, 1, 3, 2, 3}]$

Out[2]=