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/

```

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