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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.
3
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, 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, 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
OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.7 Lengyel's constant, p. 318.
LINKS
FORMULA
(Sum_(k=-infinity..infinity) q^(-k^2)) / (prod_(j>0) (1-q^(-j))), with q = 2.
EXAMPLE
7.3719688014613165091531912...
MATHEMATICA
digits = 100; EllipticTheta[3, 0, 1/2]/NProduct[1-2^(-j), {j, 1, Infinity}, WorkingPrecision -> digits + 10, NProductFactors -> digits] // RealDigits[#, 10, digits]& // First
RealDigits[EllipticTheta[3, 0, 1/2]/QPochhammer[1/2, 1/2], 10, 100][[1]] (* Vladimir Reshetnikov, Oct 17 2016 *)
PROG
(PARI) th3(x)=1 + 2*suminf(n=1, x^n^2)
th3(1/2)/prodinf(n=1, 1-2.^-n) \\ Charles R Greathouse IV, Jun 06 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved