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A030169 Decimal expansion of real number x such that y = Gamma(x) is a minimum. 5
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 (list; constant; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..99.

_Simon Plouffe_, editor, Miscellaneous Mathematical Constants Project Gutenberg, 1996.

Simon Plouffe, Minimal y of GAMMA(x)

Eric Weisstein's World of Mathematics, Gamma Function

EXAMPLE

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

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: A154478 A051261 A245275 * A239809 A203999 A199371

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

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Last modified July 30 03:16 EDT 2014. Contains 245051 sequences.