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A352619
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Decimal expansion of Sum_{k>=1} (-1)^(k+1) * zeta(2k+1)/(2k+1).
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4
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2, 7, 5, 5, 7, 5, 3, 4, 4, 4, 3, 3, 9, 9, 9, 6, 6, 2, 7, 1, 8, 9, 8, 0, 4, 3, 2, 2, 8, 5, 5, 0, 5, 8, 9, 0, 3, 8, 2, 2, 5, 9, 5, 6, 1, 9, 9, 6, 1, 5, 8, 3, 6, 1, 8, 6, 5, 0, 2, 3, 2, 2, 9, 5, 0, 1, 8, 0, 7, 1, 4, 5, 3, 3, 8, 1, 6, 1, 7, 1, 7, 5, 3, 7, 0, 4, 8, 8, 3, 6, 3, 1, 8, 9, 5, 1, 7, 3, 7
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OFFSET
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0,1
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COMMENTS
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Is there a closed-form formula for this constant as for A352527?
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REFERENCES
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Bernard Candelpergher, Ramanujan Summation of Divergent Series, Springer, 2017, p. 35.
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LINKS
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Cornel Ioan Vălean, Problema 327, La Gaceta de la Real Sociedad Matemática Española, Vol. 21, No. 2 (2018), pp. 331-343.
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FORMULA
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Equals gamma + arg(i!) (see Vălean).
Equals Sum_{k>=1} (1/k - arctan(1/k)). - Amiram Eldar, Jul 21 2022
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EXAMPLE
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0.2755753444339996627189...
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MAPLE
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evalf(gamma + argument(I!), 100);
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MATHEMATICA
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RealDigits[EulerGamma + Arg[Gamma[1 + I]], 10, 100][[1]] (* Amiram Eldar, Mar 24 2022 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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