Re: Trying to recursively define a double factorial

• To: mathgroup at smc.vnet.net
• Subject: [mg126523] Re: Trying to recursively define a double factorial
• From: James Stein <mathgroup at stein.org>
• Date: Thu, 17 May 2012 04:08:07 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201205160820.EAA23026@smc.vnet.net>

```I think the function 'dF' below is what you asked for,
but I think you did not ask for what you want.

Clear[dF];
dF[n_Integer] = 1;
dF[n_Integer] /; n > 4 := (n - 2) dF[n - 4];
Table[dF[n], {n, 1, 11, 2}]
Table[dF[n], {n, 2, 12, 2}]

Perhaps you wanted a function giving the product of all even(odd) integers
less-than-OR_EQUAL to a positive even(odd) integral argument?

On Wed, May 16, 2012 at 1:20 AM, Jorge Cantu <monsterbone at msn.com> wrote:

> My goal here is to define a recursive function for a double factorial.
>  The domain of this function is the set of positive integers.  For a
> positive even integer  n  the value DF[n] is the product of all positive
> even integers which are  <n.  For a positive odd integer   n   the value
> DF[n] is the product of all positive odd integers which are <n.
>
> I wanna make a recursive function of this double factorial without If(and
> other similar statements). Here is my work so far:
>
>
> Clear[MyF1, n];
> MyF1[1] = 1;
> MyF1[n_Integer] /; (n > 0) := MyF1[n] = n*MyF1[n - 1]
>
> Table[MyF1[k], {k, (*integer*), (*integer*)}]
>
>
>
>               How do I do this?
>
>

```

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