Local Minimum of Gamma Function on Positive Domain

Theorem

The local minimum of the Gamma function on the positive real numbers occurs at the point:

$\tuple {1 \cdotp 46163 21449 68362 34126 26595, 0 \cdotp 88560 31944 10888 70027 88159}$

The sequence of the $x$-coordinate elements is A030169 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

The sequence of the $y$-coordinate elements is A030171 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Proof


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Sources

  • 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $0,88560 31944 \ldots$
  • 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.5$: Permutations and Factorials: Figure $7$
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