Paris Constant

Author

Eric W. Weisstein
April 5, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/ParisConstant.nb.

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

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

Numerical Value

Phi[1]=1;
Phi[n_]:=Phi[n]=Sqrt[Phi[n-1]+1]

Phi/@Range[6]

RootReduce[%]

Recurrence Equation

V6

RSolve[{phi[n]==Sqrt[phi[n-1]+1],phi[1]==1},phi[n],n]

RSolve[{((phi[n])^2)==phi[n-1]+1,phi[1]==1},phi[n],n]

V7

RSolve[{((phi[n])^2)==phi[n-1]+1,phi[1]==1},phi[n],n]

Product

Numeric

Times@@N[Table[((2GoldenRatio)/(GoldenRatio+Phi[n])),{n,2,1000}],110]

c=Times@@N[Table[((2GoldenRatio)/(GoldenRatio+Phi[n])),{n,2,2000}],110]

Functional Equation

F[x]==2GoldenRatio F[GoldenRatio-(Sqrt[(GoldenRatio^2)-x])]