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.
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
KEYWORD
AUTHOR
Jean-François Alcover, Jul 02 2014
STATUS
approved