| 释义 |
Wallis FormulaThe Wallis formula follows from the Infinite Product representation of the Sine
 | (1) |
 gives
 | (2) |
 | (3) |
so
Taking the derivative of the zeta function expression gives
 | (7) |
 | |  | (8) |
Equating and squaring then gives the Wallis formula, which can also be expressed
 | (9) |
The q-Analog of the Wallis formula for  is
 | (10) |
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.
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