Difference between revisions of "Catalan's identity"

From specialfunctionswiki
Jump to: navigation, search
 
(2 intermediate revisions by the same user not shown)
Line 2: Line 2:
 
==Theorem==
 
==Theorem==
 
The following formula holds:
 
The following formula holds:
$$F_n^2 - F_{n+r} F_{n-r} = (-1)^{n-r}F_r^2,$$
+
$$F(n)^2 - F(n+r) F(n-r) = (-1)^{n-r}F(r)^2,$$
where $F_n$ denotes a [[Fibonacci numbers|Fibonacci number]].  
+
where $F(n)$ denotes the $n$th [[Fibonacci numbers|Fibonacci number]].  
  
 
==Proof==
 
==Proof==

Latest revision as of 00:52, 25 May 2017

Theorem

The following formula holds: $$F(n)^2 - F(n+r) F(n-r) = (-1)^{n-r}F(r)^2,$$ where $F(n)$ denotes the $n$th Fibonacci number.

Proof

See also

Cassini's identity

References