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A100221
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Decimal expansion of Product_{k>=1} (1-1/4^k).
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18
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6, 8, 8, 5, 3, 7, 5, 3, 7, 1, 2, 0, 3, 3, 9, 7, 1, 5, 4, 5, 6, 5, 1, 4, 3, 5, 7, 2, 9, 3, 5, 0, 8, 1, 8, 4, 6, 7, 5, 5, 4, 9, 8, 1, 9, 3, 7, 8, 3, 3, 5, 7, 3, 5, 3, 4, 0, 1, 5, 7, 2, 3, 2, 5, 7, 7, 5, 3, 3, 1, 9, 8, 4, 5, 0, 7, 9, 8, 6, 7, 5, 1, 2, 4, 8, 0, 3, 3, 4, 6, 0, 4, 8, 1, 4, 2, 8, 8, 7, 9, 0, 5
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals (1/4; 1/4)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - G. C. Greubel, Nov 30 2015
Equals sqrt(Pi/log(2)) * exp(log(2)/12 - Pi^2/(12*log(2))) * Product_{k>=1} (1 - exp(-2*k*Pi^2/log(2))) (McIntosh, 1995).
Equals Sum_{n>=0} (-1)^n/A027637(n). (End)
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EXAMPLE
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0.68853753712033971545651435729350818467554981937833...
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MATHEMATICA
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EllipticThetaPrime[1, 0, 1/2]^(1/3)/2^(1/4)
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PROG
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(PARI) prodinf(x=1, 1-1/4^x) \\ Altug Alkan, Dec 01 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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