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A243266 Decimal expansion of a parking constant related to the asymptotic expected number of cars, assuming random car lengths. 3

%I #9 Feb 14 2017 22:37:30

%S 9,8,4,8,7,1,2,8,2,5,2,5,9,9,5,3,0,4,4,7,2,7,9,5,2,2,1,5,0,7,0,5,9,5,

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

%U 3,7,9,3,8,8,4,0,7,3,1,6,0,6,4,3,1,8,7,0,0,9,7,4,9,4,6,3,0,0,6,7

%N Decimal expansion of a parking constant related to the asymptotic expected number of cars, assuming random car lengths.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.3 Renyi's parking constant, p. 279.

%H G. C. Greubel, <a href="/A243266/b243266.txt">Table of n, a(n) for n = 0..5000</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RenyisParkingConstants.html">Rényi's Parking Constants</a>

%F (1-1/2^((sqrt(17)-1)/4))*sqrt(Pi)*GAMMA(sqrt(17)/2)/(GAMMA((sqrt(17)+1)/4)*GAMMA((sqrt(17)+3)/4)^2), where GAMMA is the Euler Gamma function.

%e 0.9848712825259953044727952215...

%t (1-1/2^((Sqrt[17]-1)/4))*Sqrt[Pi]*Gamma[Sqrt[17]/2]/(Gamma[(Sqrt[17]+1)/4]*Gamma[(Sqrt[17]+3)/4]^2) // RealDigits[#, 10, 100]& // First

%o (PARI) (1-1/2^((sqrt(17)-1)/4))*sqrt(Pi)*gamma(sqrt(17)/2)/(gamma((sqrt(17)+1)/4)*gamma((sqrt(17)+3)/4)^2) \\ _G. C. Greubel_, Feb 14 2017

%Y Cf. A050996.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Jun 02 2014

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Last modified April 18 06:12 EDT 2024. Contains 371769 sequences. (Running on oeis4.)