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Question: how to get a general solution from recurrence relation

Question:how to get a general solution from recurrence relation

lxyuzs 26 Maple 14
March 22 2011
0

there are several method to provide solve recurrence problems  in Maple,such as define ,rsolve,etc.here ,i meet a problem.

i want to compute the function Gamma(n), if n is a posint ,only given recurrence relation f(z)=(z-1)f(z-1),initial condition,f(0)=1,then i can get the true result with rsolve,of couse,i had made  an ansatz that z is n::posint.yet ,z is not posint? To suppose z  equal to 5/2, (2*n+1)/2 more generally,how can get the answer((2n-1)!!*Pi/2^n).if i get the general solution,how can do ?if i have knew the f(1/3),i can get the answer of f(n+1/3)?

such as rsovle({y(n)=(n-1)*y(n-1),y(0)=1},y)
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