A175472 Decimal expansion of the absolute value of the abscissa of the local maximum of the Gamma function in the interval [ -1,0].

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

Offset: 0

Author

R. J. Mathar, May 25 2010

Keywords

• cons
• nonn

Comments

Also the location of the zero of the digamma function in the same interval.

Examples

			Gamma(-0.5040830082644554092582693045...) = -3.5446436111550050891219639933..
		

References

• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 44, page 427.

Links

• Eric Weisstein's World of Mathematics, Gamma Function.
• Wikipedia, Particular values of the Gamma function.

Crossrefs

Cf. A030169, A030171, A175473, A175474.

Programs

Mathematica

x /. FindRoot[ PolyGamma[0, x] == 0, {x, -1/2}, WorkingPrecision -> 105] // Abs // RealDigits // First  (* Jean-François Alcover, Jan 21 2013 *)

PARI

solve(x=.5,.6,psi(-x)) \\ Charles R Greathouse IV, Jul 19 2013