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holomorphic binary operators over naturals; generalized hyper operators
#8
I think the following will work to show convergeance

assume x , y and s to be reals > eta

1) the value of the product = 0 => done

2) the value is not zero => take the log => we get a sum

2b) show that the tail of the sequence goes to 0 faster than constant / n^2 hence we have convergeance. ( because of the famous Basel problem " zeta(2) = Pi^2 / 6 " )

As for the recursion , i dont know if it helps but remember

to go from s+1 to s do :

( we take the inverse with respect to y , notation : ^-1 )

f(x,y,s) = f(x,f^-1(x,y,s)+1,s)

which should be valid for all sufficiently large real non-integer s too.

regards

tommy1729
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RE: holomorphic binary operators over naturals; generalized hyper operators - by tommy1729 - 07/21/2012, 03:42 PM

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