

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*(theta1) = 5.2569464..., the fractional dimensions at which ddimensional 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: A098141 A175458 A135598 * A330576 A099506 A205001
Adjacent sequences: A244616 A244617 A244618 * A244620 A244621 A244622


KEYWORD

nonn,cons,easy


AUTHOR

JeanFrançois Alcover, Jul 02 2014


STATUS

approved



