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Student Support Forum: 'How to use Convert and GeneratingFunction?' topicStudent Support Forum > General > Archives > "How to use Convert and GeneratingFunction?"

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William
02/18/12 8:24pm

How to use Convert and GeneratingFunction?

would like to change Meixner's recurrence equation into Generating function,

but not success, after googled, it said Convert function will change something into differential equation and Dsolve

How to convert recurrence equation with variable coefficients into generating function

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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