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A344968
Decimal expansion of Sum_{k>=0} 1/(x_k^2 - x_k), where x_k is the k-th zero of the digamma function.
4
3, 4, 2, 6, 9, 8, 9, 4, 4, 4, 2, 1, 9, 9, 3, 6, 3, 3, 5, 3, 9, 8, 6, 7, 1, 8, 8, 8, 8, 2, 6, 6, 7, 1, 2, 7, 3, 3, 1, 0, 6, 3, 7, 8, 7, 9, 1, 7, 0, 2, 5, 9, 0, 1, 1, 8, 9, 1, 7, 7, 4, 0, 3, 3, 1, 6, 2, 0, 9, 4, 4, 8, 1, 5, 8, 4, 3, 3, 7, 3, 7, 2, 1, 2, 3, 7, 4
OFFSET
1,1
COMMENTS
The zeros of the digamma function, i.e., the roots of psi(x) = 0 are x_0 = 1.461632... (A030169), the only positive root, x_1 = -0.504083... (A175472), etc.
LINKS
István Mező and Michael E. Hoffman, Zeros of the digamma function and its Barnes G-function analogue, Integral Transforms and Special Functions, Vol. 28, No. 11 (2017), pp. 846-858.
Wikipedia, Digamma function.
FORMULA
Equals Pi^2/(6*gamma) + gamma, where gamma is Euler's constant (A001620).
EXAMPLE
3.42698944421993633539867188882667127331063787917025...
MATHEMATICA
RealDigits[Pi^2/(6*EulerGamma) + EulerGamma, 10, 100][[1]]
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jun 03 2021
STATUS
approved