Skip to main content
Mathematics

Return to Question

Removed from Network Questions by Asaf Karagila♦
Became Hot Network Question
Improve formatting, correct spelling of Fibonacci, remove the tag "functions".
Source Link
Jendrik Stelzner
Jendrik Stelzner
  • 16.6k
  • 4
  • 29
  • 70

How are there two generating functions for the Fibbonacci SeriesFibonacci sequence?

I've come across two generating functions for the Fibonacci Numberssequence,

$\ F(z)= \frac{1}{1-z-z^2}$ and $\ F(z)= \frac{z}{1-z-z^2}$

I've $$ F(z) = \frac{1}{1-z-z^2} \quad\text{and}\quad F(z) = \frac{z}{1-z-z^2} \,. $$ I've seen both of their proofs and both of them seem legible, but I'm still unable two understand how both the equations give same function.

How are there two generating functions for the Fibbonacci Series?

I've come across two generating functions for the Fibonacci Numbers,

$\ F(z)= \frac{1}{1-z-z^2}$ and $\ F(z)= \frac{z}{1-z-z^2}$

I've seen both of their proofs and both of them seem legible, but I'm still unable two understand how both the equations give same function.

How are there two generating functions for the Fibonacci sequence?

I've come across two generating functions for the Fibonacci sequence, $$ F(z) = \frac{1}{1-z-z^2} \quad\text{and}\quad F(z) = \frac{z}{1-z-z^2} \,. $$ I've seen both of their proofs and both of them seem legible, but I'm still unable two understand how both the equations give same function.

Source Link
Vyomi Arya
Vyomi Arya
  • 55
  • 6

How are there two generating functions for the Fibbonacci Series?

I've come across two generating functions for the Fibonacci Numbers,

$\ F(z)= \frac{1}{1-z-z^2}$ and $\ F(z)= \frac{z}{1-z-z^2}$

I've seen both of their proofs and both of them seem legible, but I'm still unable two understand how both the equations give same function.