Fibonacci Hyperbolic Functions

Author

Eric W. Weisstein
March 16, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/FibonacciHyperbolicFunctions.nb.

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Initialization

FCosh[x_]:=2/Sqrt[5]Cosh[(2x+1)Log[GoldenRatio]]
FSinh[x_]:=2/Sqrt[5]Sinh[2x Log[GoldenRatio]]
FTanh[x_]:=FSinh[x]/FCosh[x]

FSinh

Plot[FSinh[x],{x,-5,5},Epilog->{PointSize[.02],Red,Point[Table[{n,FSinh[n]},{n,-5,5}]]},PlotStyle->Red]

'

Table[FullSimplify[FSinh[n]],{n,5}]

Table[Fibonacci[2n],{n,5}]

FCosh

Plot[FCosh[x],{x,-5,5},Epilog->{PointSize[.02],Red,Point[Table[{n,FCosh[n]},{n,-4,4}]]},PlotStyle->Red]

Table[FullSimplify[FCosh[n]],{n,5}]

Table[Fibonacci[2n+1],{n,5}]

FTanh

Plot[FTanh[x],{x,-5,5},Epilog->{PointSize[.02],Red,Point[Table[{n,FTanh[n]},{n,-4,4}]]},PlotStyle->Red]

Table[FullSimplify[FTanh[n]],{n,5}]

Table[Fibonacci[2n]/Fibonacci[2n+1],{n,5}]