sum of 1/A007504(n)

[Don Reble]

Stefan Steinerberger wrote:
> Let f_n be the sum of the first n primes. Then it is easy to see that
> f_n = 2 + 3 + 5 ... + p(n) > 1 + 3 + 5 + ... + (2n-1) = n^2
> 
> Now we use this argument to get an upper bound for
> Sum[1/f_n, {i, 10^4 + 1, oo}]

    Using a slight improvement of that idea, and my CDrom full of
    primes, I can determine that

	1.023476323822197 < X < 1.023476324054903

    Argggh! It's only a microtwitch away from the next digit.



    Does anyone know how to calculate the digamma function, _very_
    accurately, for arbitrary (irrational) arguments?

-- 
Don Reble  djr at nk.ca


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