

A366166


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


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
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OFFSET

1,1


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 N2 units, whereas the other two gamblers start with one unit each. This probability is ~ c/N^3. See Diaconis link for details.


LINKS



FORMULA



EXAMPLE

4.5597944999598458154817364845572481176367423801661405635...


MATHEMATICA

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


PROG

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


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



