My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum

LinkBack Thread Tools Display Modes
December 24th, 2011, 04:08 AM   #1
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?
Emilijo is offline  
December 24th, 2011, 01:37 PM   #2
Global Moderator
CRGreathouse's Avatar
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.
CRGreathouse is offline  
December 25th, 2011, 12:40 PM   #3
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.
Emilijo is offline  

  My Math Forum > College Math Forum > Number Theory

nth, term

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
the 12 term of a G.P kingkos Algebra 2 December 21st, 2012 08:19 PM
Sum to nth term rnck Applied Math 3 August 23rd, 2012 08:17 PM
Term by term differentiation forcesofodin Real Analysis 4 August 14th, 2010 06:50 PM
Please help what term to use Algebra 1 September 25th, 2008 09:29 AM
Sum to nth term rnck Real Analysis 3 December 31st, 1969 04:00 PM

Copyright © 2019 My Math Forum. All rights reserved.