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A030169 Decimal expansion of real number x such that y = Gamma(x) is a minimum. 20
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
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
KEYWORD
nonn,cons
AUTHOR
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 June 22 06:24 EDT 2024. Contains 373565 sequences. (Running on oeis4.)