A030169 Decimal expansion of real number x such that y = Gamma(x) is a minimum.

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

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

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.4, p. 34.

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