Re: Trying to recursively define a double factorial

*To*: mathgroup at smc.vnet.net*Subject*: [mg126528] Re: Trying to recursively define a double factorial*From*: Peter Breitfeld <phbrf at t-online.de>*Date*: Thu, 17 May 2012 04:09:51 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jovo6m$mhq$1@smc.vnet.net>

Jorge Cantu 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? > This should work: Clear[myF] myF[-1] = 1 myF[0] = 1 myF[1] = 1; myF[n_Integer?Positive] := myF[n] = n myF[n - 2] Compare with build in !!: Table[{myF[k], k!!}, {k, 1, 10}] Output: {{1, 1}, {2, 2}, {3, 3}, {8, 8}, {15, 15}, {48, 48}, {105, 105}, {384, 384}, {945, 945}, {3840, 3840}} -- _________________________________________________________________ Peter Breitfeld | Bad Saulgau, Germany | http://www.pBreitfeld.de