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A241011
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Decimal expansion of Sierpiński's S~ (S "tilde" as named by S. Finch), a constant appearing in the asymptotics of the number of representations of a positive integer as a sum of two squares.
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2
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2, 0, 1, 6, 6, 2, 1, 5, 4, 5, 7, 3, 3, 4, 0, 8, 1, 1, 5, 2, 6, 2, 7, 9, 6, 8, 5, 9, 7, 1, 5, 1, 1, 5, 4, 2, 6, 4, 5, 0, 1, 8, 4, 1, 7, 7, 5, 2, 3, 6, 4, 7, 4, 8, 0, 6, 1, 0, 9, 1, 9, 2, 8, 3, 4, 4, 7, 8, 1, 4, 3, 4, 1, 6, 1, 6, 1, 8, 2, 7, 8, 7, 2, 5, 5, 4, 1, 3, 5, 1, 3, 9, 8, 3, 0, 6, 1, 8, 0, 4
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OFFSET
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1,1
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COMMENTS
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4*gamma - 1 + log(2)/3 - 2*log(Pi) + 8*log(Gamma(3/4)) - 12*Zeta'(2)/Pi^2 = 2.01662154573340811526279685971511542645018417752364748061...
The constant C, published by Ramanujan (1916, formula (22)), 4*gamma - 1 + log(2)/3 - log(Pi) + 4*log(Gamma(3/4)) - 12*Zeta'(2)/Pi^2 = 2.3482276258576268... is wrong! (End)
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.10 Sierpinski's constant, p. 122.
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LINKS
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FORMULA
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S_tilde = 2*S - 12/Pi^2*zeta'(2) + log(2)/3 - 1, where S = A086058 - 1 = A062089 / Pi.
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EXAMPLE
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2.01662154573340811526279685971511542645018417752364748061...
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MATHEMATICA
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S = 2*EulerGamma + 2*Log[2] + 3*Log[Pi] - 4* Log[Gamma[1/4]]; (* S~ *) St = 2*S - 12/Pi^2*Zeta'[2] + Log[2]/3 - 1; RealDigits[St, 10, 100] // First
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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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