*N.B. A detailed on-line essay by S. Finch
was 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) |

(4) | |||

(5) |

(Blatner 1997).

The product

(6) |

(7) | |||

(8) | |||

(9) | |||

(10) |

The

(11) |

(12) | |||

(13) | |||

(14) | |||

(15) |

**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.

© 1996-9

1999-05-26