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A242056 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). 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.32 De Bruijn-Newman constant, p. 203.

LINKS

Table of n, a(n) for n=1..105.

Steven R. Finch, Errata and Addenda to Mathematical Constants. 2.32 p. 27.

Jeffrey C. Lagarias and David Montague, The Integral of the Riemann xi-function. arXiv:1106.4348 [math.NT], 2011.

Jeffrey C. Lagarias and David Montague, The Integral of the Riemann xi-function, Commentarii Mathematici Universitatis Sancti Pauli 60 (2011), No. 1-2, pp. 143-169.

FORMULA

Equals 2*Pi*sum_{n>=1} (Pi*n^2*(2*Pi*n^2-3))/e^(Pi*n^2).

EXAMPLE

2.8066794017776921830509142738181545641549800285022563559424697...

MATHEMATICA

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

PROG

(PARI) 2*Pi*suminf(n=1, t=Pi*n^2; t*(2*t-3)/exp(t)) \\ Charles R Greathouse IV, Mar 10 2016

CROSSREFS

Sequence in context: A188924 A011055 A268813 * A195009 A337997 A020860

Adjacent sequences:  A242053 A242054 A242055 * A242057 A242058 A242059

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Aug 13 2014

STATUS

approved

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Last modified January 27 05:50 EST 2022. Contains 350601 sequences. (Running on oeis4.)