A366166 Decimal expansion of sqrt(Pi)/(3*sqrt(3))*(Gamma(1/3)/Gamma(5/6))^3.

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

Offset: 1

Author

Hugo Pfoertner, Oct 13 2023

Keywords

• nonn
• cons

Comments

This constant c occurs in the probability that the "big player" in a game with 3 gamblers goes broke first, although he starts with an initial capital of N-2 units, whereas the other two gamblers start with one unit each. This probability is ~ c/N^3. See Diaconis link for details.

Examples

			4.5597944999598458154817364845572481176367423801661405635...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Persi Diaconis, Gambler's ruin with k gamblers (slide 3), talk in the Rutgers Experimental Mathematics Seminar, Fall 2023 Semester, Oct. 12, 2023.

Crossrefs

Cf. A059231, A366566, A366567.

Programs

Mathematica

First[RealDigits[Gamma[1/3]^9/(2Pi)^4,10,100]] (* Paolo Xausa, Oct 14 2023 *)

PARI

sqrt(Pi)/(3*sqrt(3))*(gamma(1/3)/gamma(5/6))^3

Formula

Equals Gamma(1/3)^9 / (2*Pi)^4. - Peter Luschny, Oct 13 2023