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A242056
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Decimal expansion of 2*Pi*phi(0), a constant appearing in connection with a study of zeros of the integral of xi(z), where phi(t) and xi(z) are functions related to Riemann's zeta function (see Finch reference for the definition of these functions).
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1
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2, 8, 0, 6, 6, 7, 9, 4, 0, 1, 7, 7, 7, 6, 9, 2, 1, 8, 3, 0, 5, 0, 9, 1, 4, 2, 7, 3, 8, 1, 8, 1, 5, 4, 5, 6, 4, 1, 5, 4, 9, 8, 0, 0, 2, 8, 5, 0, 2, 2, 5, 6, 3, 5, 5, 9, 4, 2, 4, 6, 9, 7, 1, 2, 7, 0, 6, 9, 9, 2, 2, 6, 5, 6, 0, 1, 3, 8, 3, 0, 2, 1, 8, 2, 2, 4, 4, 8, 9, 6, 6, 2, 3, 0, 3, 6, 2, 6, 6, 0, 9, 6, 6, 5, 3
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OFFSET
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1,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.32 De Bruijn-Newman constant, p. 203.
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LINKS
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FORMULA
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Equals 2*Pi*sum_{n>=1} (Pi*n^2*(2*Pi*n^2-3))/e^(Pi*n^2).
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EXAMPLE
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2.8066794017776921830509142738181545641549800285022563559424697...
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MATHEMATICA
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digits = 105; 2*Pi*NSum[(Pi*n^2*(2*Pi*n^2-3))/E^(Pi*n^2), {n, 1, Infinity}, WorkingPrecision -> digits+5] // RealDigits[#, 10, digits]& // First
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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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