The q-Analog of the Cosine function, as advocated by R. W. Gosper, is defined by
where
is a Theta Function and is defined via
This is a period , Even Function of unit amplitude with double and triple angle formulas and addition formulas which
are analogous to ordinary Sine and Cosine. For example,
where is the q-Sine, and is q-Pi. The -cosine also satisfies
See also q-Factorial, q-Sine
References
Gosper, R. W. ``Experiments and Discoveries in -Trigonometry.'' Unpublished manuscript.
© 1996-9 Eric W. Weisstein
1999-05-25