d'Ocagne's Identity

Author

Eric W. Weisstein
March 6, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/dOcagnesIdentity.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/dOcagnesIdentity.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Identity

(Subscript[F, n+1]) (Subscript[F, m])-(Subscript[F, m+1]) (Subscript[F, n])=(((-1))^n) (Subscript[F, m-n])

FullSimplify[FunctionExpand[Fibonacci[m]Fibonacci[n+1]-Fibonacci[n]Fibonacci[m+1]-(-1)^n Fibonacci[m-n]]]

FullSimplify[%,(m|n)∈Integers]