A030171 Decimal expansion of real number y such that y = Gamma(x) is a minimum.

8, 8, 5, 6, 0, 3, 1, 9, 4, 4, 1, 0, 8, 8, 8, 7, 0, 0, 2, 7, 8, 8, 1, 5, 9, 0, 0, 5, 8, 2, 5, 8, 8, 7, 3, 3, 2, 0, 7, 9, 5, 1, 5, 3, 3, 6, 6, 9, 9, 0, 3, 4, 4, 8, 8, 7, 1, 2, 0, 0, 1, 6, 5, 8, 7, 5, 1, 3, 6, 2, 2, 7, 4, 1, 7, 3, 9, 6, 3, 4, 6, 6, 6, 4, 7, 9, 8, 2, 8, 0, 2, 1, 4, 2, 0, 3, 5, 9

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn
• cons

Examples

			0.885603194410888700278815900582588733207951533669903448871200165875136...
		

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 = 0..5000
• Simon Plouffe, Minimal point of GAMMA(x).
• Simon Plouffe, Minimal y of GAMMA(x).
• Eric Weisstein's World of Mathematics, Gamma Function.

Crossrefs

Cf. A030169 for value of x.

Programs

Maple

Digits:=500; x0:=fsolve(Psi(x)=0, x); evalf(GAMMA(x0), 120) # Iaroslav V. Blagouchine, Feb 16 2016

Mathematica

First@ RealDigits[ FindMinimum[ Gamma[x], {x, 1.4}, WorkingPrecision -> 2^7][[1]]] (* Robert G. Wilson v, Aug 03 2010 *)
RealDigits[ Gamma[x /. FindRoot[ PolyGamma[0, x] == 0, {x, 1}, WorkingPrecision -> 100]]][[1]] (* Jean-François Alcover, Oct 23 2012 *)

PARI

gamma(solve(x=1,2,psi(x))) \\ Charles R Greathouse IV, Apr 17 2015