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.

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

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

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

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: A175458 A356080 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