|
| |
|
|
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
|
| |
|
|
