Gaussian Bracket

Author

Eric W. Weisstein
March 22, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheory/GaussianBrackets.nb.

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

©2009 Wolfram Research, Inc. except for portions noted otherwise

Code

GaussianBracket[]:=1
GaussianBracket[a_]:=a
GaussianBracket[a1_,a2_]:=GaussianBracket[a1]a2+GaussianBracket[]
GaussianBracket[a1_,a2__,a3_]:=GaussianBracket@@Prepend[{a2},a1]a3+GaussianBracket@@Prepend[Most[{a2}],a1]

Identities

GaussianBracket[]

Table[GaussianBracket@@Array[a,n],{n,0,6}]/.a[n_]:>Subscript[a,n]//Column//TraditionalForm

Subtract@@@Table[{((Gauss[Rest[l=Array[a,n]]])/(Gauss[l])),ContinuedFractionK[a[k],{k,n}]},{n,10}]//FullSimplify