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A242938 Decimal expansion of c_e, coefficient associated with the asymptotic evaluation c_e*2^(n^2/4) of the number of subspaces of the n-dimensional vector space over the finite field F_2, n being even.

%I A242938 #16 Oct 17 2016 17:07:04
%S A242938 7,3,7,1,9,6,8,8,0,1,4,6,1,3,1,6,5,0,9,1,5,3,1,9,1,2,0,8,2,6,8,0,9,1,
%T A242938 5,8,8,8,5,8,7,6,3,5,4,7,2,2,6,6,2,2,6,6,8,9,4,3,5,4,6,1,0,4,2,3,1,0,
%U A242938 1,5,6,7,4,3,0,0,0,7,2,8,9,4,4,7,5,7,0,8,8,2,4,7,8,0,5,5,6,9,9,5
%N A242938 Decimal expansion of c_e, coefficient associated with the asymptotic evaluation c_e*2^(n^2/4) of the number of subspaces of the n-dimensional vector space over the finite field F_2, n being even.
%D A242938 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.7 Lengyel's constant, p. 318.
%H A242938 G. C. Greubel, <a href="/A242938/b242938.txt">Table of n, a(n) for n = 1..2500</a>
%F A242938 (Sum_(k=-infinity..infinity) q^(-k^2)) / (prod_(j>0) (1-q^(-j))), with q = 2.
%e A242938 7.3719688014613165091531912...
%t A242938 digits = 100; EllipticTheta[3, 0, 1/2]/NProduct[1-2^(-j), {j, 1, Infinity}, WorkingPrecision -> digits + 10, NProductFactors -> digits] // RealDigits[#, 10, digits]& // First
%t A242938 RealDigits[EllipticTheta[3, 0, 1/2]/QPochhammer[1/2, 1/2], 10, 100][[1]] (* _Vladimir Reshetnikov_, Oct 17 2016 *)
%o A242938 (PARI) th3(x)=1 + 2*suminf(n=1,x^n^2)
%o A242938 th3(1/2)/prodinf(n=1,1-2.^-n) \\ _Charles R Greathouse IV_, Jun 06 2016
%Y A242938 Cf. A048651, A086053, A242939, A182176.
%K A242938 nonn,cons
%O A242938 1,1
%A A242938 _Jean-François Alcover_, May 27 2014