Exponential Generating Functions

Click For Summary

Homework Help Overview

The discussion revolves around understanding a step in the manipulation of exponential generating functions, specifically focusing on the transition between two steps in a solution involving binomial expansion.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand how a summation is introduced in the solution process. Some participants provide insights into the use of binomial expansion related to exponential generating functions.

Discussion Status

Participants are engaging in clarifying the steps involved in the problem. One participant has pointed out the binomial expansion, which may help guide the original poster's understanding. There is a recognition of different approaches to derive the same result, but no explicit consensus has been reached.

Contextual Notes

The original poster expresses confusion about the transition between steps in the solution, indicating a potential gap in understanding the application of exponential generating functions and their properties.

kensaurus
Messages
9
Reaction score
0
I got a question here, and I am stuck at understanding the step of the solution. Any help will be appreciated.

http://img841.imageshack.us/img841/6589/40155869.jpg

I would like to know how to get from the second to the third step, where the summation comes in.

It looks like multiplication of 2 exponential generating function, but the second step is not one. Thanks for any help.
 
Last edited by a moderator:
Physics news on Phys.org
the second step is the binomial expansion of [itex](e^x-1)^k[/itex].

cheers
 
oh my, I am slapping my head... i went to derive it through complex, exponential functions and other means...

thanks a lot!
 
cheers.
 

Similar threads

Calculate (and argue) the critical points of an exponential function
  • · Replies 10 ·
Replies
10
Views
2K
Evaluating an integral of an exponential function
  • · Replies 3 ·
Replies
3
Views
2K
A game of roulette and generating functions
  • · Replies 3 ·
Replies
3
Views
2K
Prove this inequality using induction
  • · Replies 2 ·
Replies
2
Views
2K
Fourier transform of exponential function
  • · Replies 3 ·
Replies
3
Views
3K
Finding the generator function for 4 variables
  • · Replies 3 ·
Replies
3
Views
1K
Linear Algebra - Prove that E is not a basis for V.
  • · Replies 9 ·
Replies
9
Views
2K
Exponential curve fit using Apache Commons Math
  • · Replies 9 ·
Replies
9
Views
6K
Deriving the particle's motion using numerical integration
  • · Replies 5 ·
Replies
5
Views
942
Integration of an exponential function
  • · Replies 4 ·
Replies
4
Views
2K