The Wallis formula follows from the Infinite Product representation of the Sine
(1) |
(2) |
(3) |
(4) | |||
(5) |
(6) |
(7) |
(8) |
(9) |
The q-Analog of the Wallis formula for is
(10) |
See also Wallis Cosine Formula, Wallis Sine Formula
References
Abramowitz, M. and Stegun, C. A. (Eds.).
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, p. 258, 1972.
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/dig/dig.html
Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 63-64, 1951.
© 1996-9 Eric W. Weisstein