December 24th, 2011, 03:08 AM  #1 
Newbie Joined: Nov 2011 Posts: 20 Thanks: 0  nth term
If I have generating function, nth term of its series is given by formula: c_n=(f^(n) (0) )/n! Problem is f^(n), nth derivative of generating function, specially if generating function is quotient of two functions. Is there a formula for nth term of series that will not be difficult to calculate with it? 
December 24th, 2011, 12:37 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: nth term
It's very easy to take the derivative of a gf  just remove the constant term, multiply all remaining terms by their exponents, and reduce exponents by 1. The generalization to second, ... derivatives is easy; you can write out the multiple using the factorial function if you like.

December 25th, 2011, 11:40 AM  #3 
Newbie Joined: Nov 2011 Posts: 20 Thanks: 0  Re: nth term
i.e. generating function is f(x)=(sum_(k=1,to m1) x^k)/(1x^m), where m is period; 0,1,1,0,1,1... m=3 0,1,1,1,0,1,1,1,0... m=4... What is nth of the series given by the generating function? Formula must be general, so I can just put m. 

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