A030169 Decimal expansion of the real positive number x such that 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
Examples
x = 1.461632144968362..., Gamma(x) = 0.885603194410888...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.4, p. 34.
- Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 44, page 427.
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.
Crossrefs
Cf. A030171 for value of Gamma(x).
Programs
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Maple
Digits:= 120; fsolve(Psi(x)=0, x); # Iaroslav V. Blagouchine, Feb 16 2016
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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 *) -
PARI
solve(x=1,2,psi(x)) \\ Charles R Greathouse IV, May 30 2012
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
Comments