How to convert recurrence into generating function?

• To: mathgroup at smc.vnet.net
• Subject: [mg125040] How to convert recurrence into generating function?
• From: Lee Martin <galeomaga at gmail.com>
• Date: Sun, 19 Feb 2012 06:30:26 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```there is an Mexiner recurrence equation,
but both generatingfunction and convert not convert into generating
function as stated in paper.

How to recurrence into generating function correctly?

GeneratingFunction[c*(n+beta)*P(n+1)/(-1+c)+(c*(x+beta)/(1-c)-x)*P(n)
+n*P(n-1)/(-1+c) = 0,n,z]
GeneratingFunction[c*(n+beta)*P(n+1)/(-1+c)+(c*(x+beta)/(1-c)-x)*P(n)
+n*P(n-1)/(-1+c),n,z]

Expand((c*(n+beta)*P[n+1]/(-1+c)+(c*(x+beta)/(1-c)-x)*P[n]+n*P[n-1]/
(-1+c))*z^n/n!)

Convert[sum[z^n*c*P[n+1]*n/(n!*(-1+c))+z^n*c*P[n+1]*beta/(n!*(-1+c))
+z^n*P[n]*c*x/(n!*(1-c))+z^n*P[n]*c*beta/(n!*(1-c))-z^n*P[n]*x/n!
+z^n*n*P[n-1]/(n!*(-1+c)),{n,0,infinity}],z]
Convert[sum[(c*(n+beta)*P[n+1]/(-1+c)+(c*(x+beta)/(1-c)-x)*P[n]
+n*P[n-1]/(-1+c))*z^n/n!,{n,0,infinity}],z]

```

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