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 A244619 Decimal expansion of 'theta', the unique positive root of the equation polygamma(x) = log(Pi), where polygamma(x) gives gamma'(x)/gamma(x), that is the logarithmic derivative of the gamma function. 0
 3, 6, 2, 8, 4, 7, 3, 2, 0, 2, 4, 3, 0, 2, 8, 8, 3, 9, 0, 0, 6, 6, 4, 1, 9, 1, 9, 4, 3, 4, 5, 3, 8, 4, 6, 1, 8, 3, 0, 9, 5, 0, 8, 6, 1, 8, 5, 9, 1, 6, 0, 7, 4, 2, 8, 7, 5, 4, 9, 3, 9, 8, 3, 9, 3, 8, 8, 5, 5, 4, 6, 7, 3, 3, 6, 8, 4, 1, 0, 1, 3, 6, 4, 0, 8, 8, 6, 0, 1, 1, 9, 2, 4, 4, 8, 9, 6, 2, 3, 4, 6, 3, 4, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This constant appears in d_a = 2*theta = 7.2569464... and d_v = 2*(theta-1) = 5.2569464..., the fractional dimensions at which d-dimensional spherical surface area and volume, respectively, are maximized. [after Steven Finch] REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.5.4 Gamma Function, p. 34. LINKS EXAMPLE 3.6284732024302883900664191943453846183... MATHEMATICA theta = x /. FindRoot[PolyGamma[x] == Log[Pi], {x, 4}, WorkingPrecision -> 105]; RealDigits[theta] // First PROG (PARI) polygamma(n, x) = if (n == 0, psi(x), (-1)^(n+1)*n!*zetahurwitz(n+1, x)); solve(x=3.5, 3.7, polygamma(0, x) - log(Pi)) \\ Gheorghe Coserea, Sep 30 2018 CROSSREFS Cf. A074454, A074455, A074456, A074457. Sequence in context: A098141 A175458 A135598 * A330576 A099506 A205001 Adjacent sequences:  A244616 A244617 A244618 * A244620 A244621 A244622 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Jul 02 2014 STATUS approved

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Last modified April 19 17:04 EDT 2021. Contains 343116 sequences. (Running on oeis4.)