Infinite Product
N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
A Product involving an Infinite number of terms. Such products can converge. In fact, for Positive
, the Product 
converges to a Nonzero number Iff 
converges.
Infinite products can be used to define the Cosine
 | (1) |
 | (2) |
 | (3) |
and the 
th Prime 
is |  |  | (4) |
|  | (5) |
(Blatner 1997).
The product
 | (6) |
, | |  | (7) |
 | |  | (8) |
 | |  | (9) |
 | |  | (10) |
The d-Analog expression
 | (11) |
 | |  | (12) |
 | |  | (13) |
 | |  | (14) |
 | |  | (15) |
See also Cosine, Dirichlet Eta Function, Euler Identity, Gamma Function, IteratedExponential Constants, Polygon Circumscribing Constant, Polygon Inscribing Constant, Q-Function,Sine
References
Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 75, 1972. Arfken, G. ``Infinite Products.'' §5.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 346-351, 1985. Blatner, D. The Joy of Pi. New York: Walker, p. 119, 1997. Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/infprd/infprd.html Hansen, E. R. A Table of Series and Products. Englewood Cliffs, NJ: Prentice-Hall, 1975. Whittaker, E. T. and Watson, G. N. §7.5 and 7.6 in A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.
- Combinatorial Topology
- Combinatorics
- Comma Derivative
- Comma of Didymus
- Comma of Pythagoras
- Common Cycloid
- Common Residue
- Commutation Coefficient
- Commutative
- Commutative Algebra
- Commutator
- Compact Group
- Compact Manifold
- Compactness Theorem
- Compact Set
- Compact Space
- Compact Surface
- Companion Knot
- Comparability Graph
- Comparison Test
- Compass
- Compatible
- Complementary Angle
- Complement Graph
- Complement Knot