My Math Forum nth term

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 December 24th, 2011, 04:08 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, 01:37 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, 12:40 PM #3 Newbie   Joined: Nov 2011 Posts: 20 Thanks: 0 Re: nth term i.e. generating function is f(x)=(sum_(k=1,to m-1) x^k)/(1-x^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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### nth term differentiation

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