Creating and defining a family of functions with indexed variables?

Question

I am trying to do the following: Create a list as

Table[Subscript[\[Beta], i] _, {i, 1, dim}]

And then use this list to define a function:

F[Table[Subscript[\[Beta], i] _, {i, 1, dim}]] := something in term of beta_i

But this is not working. My main objective is to define and use a family of functions in terms of $\{\beta_1 ,\dots , \beta_n\}$ like $F_1(\{b_1,\dots ,\beta_n\}), \dots ,F_m(\{b_1,\dots ,\beta_n\})$.

How can I do that?

Answer 1

as far as I know, you can't define functions inside Table or a Do loop. Unless there is a hack to do it.

My main objective is to define and use a family of functions

Why not define the function F itself to take its id as part of the definition? As a meta function. Like this

F[i_,Subscript[β_,i_],Subscript[b_,i_]]:=Subscript[β,i]+i+i*Subscript[b,i]

And now, if you wan to call $F_2$ for example, you do

i = 2;
F[i, Subscript[β, i], Subscript[b, i]]

If you want to make different definitions for each $F_i, depending on the value of i, you can do something like this

F[i_Integer, Subscript[β_, i_], Subscript[b_, i_]] := Module[{},
  Which[i == 1, Subscript[β, i] + i + i*Subscript[b, i],
   i == 2, Subscript[β, i] + 3*i - i*2*Subscript[b, i]
   (*add more F_i special definitions here*)
   ]
  ]

Which looks like this

And now can do

and so on. btw, the sooner you avoid subscripted variable, the better it is. I never found any use for them and they cause more trouble than worth it.