Using RSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg9074] Using RSolve*From*: "Nguyen N. Anh" <anh at chm.ulaval.ca>*Date*: Thu, 9 Oct 1997 01:42:53 -0400*Sender*: owner-wri-mathgroup at wolfram.com

We have the following problem: << DiscreteMath`RSolve` In[4]:= RSolve[{a[n+1]==(n+1) a[n],a[0]==C},a[n],n] Out[4]= {{a[n] -> C n!}} This is OK. Suppose now that we want to solve the following: In[5]:= RSolve[{a[n+1]==(n+1) a[n] b[n],a[0]==C},a[n],n] with b[n] being symbolically a vector of parameters (not specified by a recurence relation), then we obtain Out[5]= RSolve[{a[n + 1] == (n + 1) a[n] b[n], a[0] == C}, a[n], n] i.e. RSolve does not work in this case. How to make this work (we want to absolutely keep b[n] in its symbolic form, i.e. to avoid prescribing a specific n-dependence for it)? Expected: Out[5]= {{a[n] -> C n! Product[b[i], {i, 0, n}]}} Thank you for your help -- Nguyen Nam Anh Quebec, Canada E-mail: anh at chm.ulaval.ca WWW: http://promethium.chm.ulaval.ca/~anh/