Variant of Wallis' product--anybody know who first found this?

Discussion in 'Recreational Math' started by Michael O'Brien, Dec 5, 2004.

  1. I happened to stumble across this variant of Wallis' product formula for pi
    some years ago:

    pi = k * sin(pi/k) * Product(k^2 * n^2 / [(kn-1)(kn+1)], n, 1, inf)

    Does anybody know who first discovered this formula?

    It should be noted that the formula leads to

    pi = 2 * sqrt(2) * [(4/3)(4/5)(8/7)(8/9)(12/11)(12/13)...] (k=4)
    pi = 3 * [(6/5)(6/7)(12/11)(12/13)(18/17)(18/19)...] (k=6)
    Michael O'Brien, Dec 5, 2004
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