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Infinite function definitions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104008] Infinite function definitions
  • From: tzygmund mcfarlane <tzygmund at googlemail.com>
  • Date: Thu, 15 Oct 2009 07:18:00 -0400 (EDT)

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.


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