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Re: Prime numbers and pi
Posted:
Apr 13, 2009 6:47 AM
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The infinite pi multiplication of Wallis mentioned by
James A. Landau can be given as a stairway approximation:
2 x 3/2
2 x 4/3 x 7/6
2 x 4/3 x 16/15 x 11/10
2 x 4/3 x 16/15 x 36/35 x 15/14
2 x 4/3 x 16/15 x 36/35 x 64/63 x 19/18
2 x 4/3 x 16/15 x 36/35 x 64/63 x 100/99 x 23/22
and so on. The numbers of the last terms of each line
increase by 4, and are then replaced by new terms
whose numbers are bigger by 1x1, 3x3, 5x5, 7x7, 9x9,
and so on. I am trying to find a regular pattern for
the infinite pi product of Euler involving the primes,
but I think I won't succeed.
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