

A030169


Decimal expansion of real number x such that y = Gamma(x) is a minimum.


14



1, 4, 6, 1, 6, 3, 2, 1, 4, 4, 9, 6, 8, 3, 6, 2, 3, 4, 1, 2, 6, 2, 6, 5, 9, 5, 4, 2, 3, 2, 5, 7, 2, 1, 3, 2, 8, 4, 6, 8, 1, 9, 6, 2, 0, 4, 0, 0, 6, 4, 4, 6, 3, 5, 1, 2, 9, 5, 9, 8, 8, 4, 0, 8, 5, 9, 8, 7, 8, 6, 4, 4, 0, 3, 5, 3, 8, 0, 1, 8, 1, 0, 2, 4, 3, 0, 7, 4, 9, 9, 2, 7, 3, 3, 7, 2, 5, 5, 9
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OFFSET

1,2


COMMENTS

"The gamma function has a minimum at this point. 1.461632144968362341262659542325721328468196204006446351295988409 is the solution of the equation: Psi(x)*GAMMA(x)=0. The point y of that function is 0.8856031944108887002788159005825887332079515336699034488712001659".  Simon Plouffe
Positive root of psi(x) = 0, where psi is the digamma function.  Charles R Greathouse IV, May 30 2012


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000
Simon Plouffe, editor, Miscellaneous Mathematical Constants Project Gutenberg, 1996 [see "Minimal y of GAMMA(x)" paragraph].
Eric Weisstein's World of Mathematics, Gamma Function


EXAMPLE

x = 1.461632144968362..., y = 0.885603194410888...


MAPLE

Digits:= 120; fsolve(Psi(x)=0, x); # Iaroslav V. Blagouchine, Feb 16 2016


MATHEMATICA

First@ RealDigits[ FindMinimum[ Gamma[x], {x, 1.4}, WorkingPrecision > 2^7][[2, 1, 2]]] (* Robert G. Wilson v, Aug 03 2010 *)
RealDigits[x /. FindRoot[PolyGamma[x], {x, 1}, WorkingPrecision > 200]][[1]] (* Charles R Greathouse IV, May 30 2012 *)


PROG

(PARI) solve(x=1, 2, psi(x)) \\ Charles R Greathouse IV, May 30 2012


CROSSREFS

Cf. A030171 for value of y.
Sequence in context: A051261 A247621 A245275 * A263180 A239809 A203999
Adjacent sequences: A030166 A030167 A030168 * A030170 A030171 A030172


KEYWORD

nonn,cons


AUTHOR

Eric W. Weisstein


EXTENSIONS

Additional comments from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 29 2001
Broken URL to Project Gutenberg replaced by Georg Fischer, Jan 03 2009


STATUS

approved



