This document discusses mathematical generating functions. It defines a generating function as treating the coefficients of an infinite sequence as coefficients in a series expansion, with the sum of the series being the generating function. It discusses ordinary generating functions specifically, where the generating function is a power series representing a sequence. Some examples of sequences and their generating functions are given. It also notes that adding leading zeros to a sequence corresponds to multiplying the generating function by x to the power of the number of zeros added, known as a right shift rule.

1. Md. Shamim Hossain
ID: 153015013
Sub: Mathmathetical Analyses
Dept: CSE
Green university of Bangladesh
Welcome To My Presentation

2. Topic
Generating Function

3. Outline
Generating Function
Ordinary Generation Function
Generating Addition Rule
Right Shifting Rule
Derivative Rule
Product Rule

4. Generating function In mathematics, the term generating function is
used to describe an infinite sequence of numbers (an) by treating
them as the coefficients of a series expansion. The sum of this
infinite series is the generating function.
Generating Function:
Example:

5. Ordinary Generation Function:
Ordinary generating function (OGF) When the term generating
function is used without qualification, it is usually taken to
mean an ordinary generating function.
The ordinary generating function for the infinite sequence
hg0,g1,g2,g3 ...i is the power series:
G(x)= g0 +g1x+g2x 2 +g3x
3 +··· .
For example, here are some sequences and their generating
functions:
h0,0,0,0,...i ←→ 0+0x+0x 2 +0x =0
3 +··· h1,0,0,0,...i ←→ 1+0x+0x 2 +0x =1
3 +···
2

6. Right Shift:
Evidently, adding k leading zeros to the sequence corresponds to multiplying the
generating function by x k. This holds true in general.