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Infinite product

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)gamma function(2)sine, and sinc function.They also appear in polygon circumscribing,(3)An interesting infinite product formula due to Euler which relates and the th prime is(4)(5)(Blatner 1997). Knar's formula gives a functional equation for the gamma function in terms of the infinite product(6)A regularized product identity is given by(7)(Muñoz Garcia and Pérez-Marco 2003, 2008).Mellin's formula states(8)where is the digamma function and is the gamma function.The following class of products(9)(10)(11)(12)(13)(Borwein et al. 2004, pp. 4-6), where is the gamma function, the first of which is given in Borwein and Corless (1999), can be done analytically. In particular, for ,(14)where (Borwein et..

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