Re: Infinite function definitions

• To: mathgroup at smc.vnet.net
• Subject: [mg104080] Re: Infinite function definitions
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Sun, 18 Oct 2009 05:23:56 -0400 (EDT)
• References: <hb709k\$8rl\$1@smc.vnet.net>

```tzygmund mcfarlane wrote:
> Hi,
>
> I am trying to do something basic, but am unable to. I would like to
> define a sequence of functions indexed by \[DoubleStruckCapitalZ]^+.
> So (pseudo-code):
>
>
> for j in {1,2,...}
>     Subscript[\[Psi], j] := Subscript[f, j][x_] := 1/x^j (** something
> slightly more complex than this; direct substitution below difficult
> **)
> end
>
> I then want to use the Subscript[\[Psi], j] as coefficients in further
> calculations (according to the values of the parameter 'x'). So (say)
> something like:
>
> x=10
> Sum[Subscript[\[Psi], j] y^j, {j, 1, Infinity}]/Sum[y^j, {j, 1,
>   Infinity}]
>
> Is this possible?
>
> Thanks.
>
Well, clearly if you set up the values of Subscript[\[Psi], j] in a
loop, you can only create finitely many of them, so a Sum to infinity
isn't going to work. Perhaps you need to explain a little more.

David Bailey
http://www.dbaileyconsultancy.co.uk

```

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