Difference between revisions of "Catalan's identity"
From specialfunctionswiki
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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 | + | where $F_n$ denotes the $n$th [[Fibonacci numbers|Fibonacci number]]. |
==Proof== | ==Proof== | ||
Revision as of 00:33, 24 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.
