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A030169
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Decimal expansion of real number x such that y = Gamma(x) is a minimum.
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12
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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
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1,2
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COMMENTS
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"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
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LINKS
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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
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EXAMPLE
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x = 1.461632144968362..., y = 0.885603194410888...
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MAPLE
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Digits:= 120; fsolve(Psi(x)=0, x); # Iaroslav V. Blagouchine, Feb 16 2016
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MATHEMATICA
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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 *)
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PROG
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(PARI) solve(x=1, 2, psi(x)) \\ Charles R Greathouse IV, May 30 2012
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CROSSREFS
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Cf. A030171 for value of y.
Sequence in context: A051261 A247621 A245275 * A263180 A239809 A203999
Adjacent sequences: A030166 A030167 A030168 * A030170 A030171 A030172
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KEYWORD
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nonn,cons,changed
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Additional comments from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 29 2001
Broken URL to Project Gutenberg replaced by Georg Fischer, Jan 03 2009
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STATUS
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approved
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