login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A030169 Decimal expansion of real number x such that y = Gamma(x) is a minimum. 12
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...

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 5 13:49 EST 2016. Contains 278768 sequences.