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A106333
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Decimal expansion of the constant x that satisfies: F(x) - x*F'(x) = 0, where F(x) = Sum_{n>=0} x^(n*(n+1)/2).
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4
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6, 4, 1, 1, 8, 0, 3, 8, 8, 4, 2, 9, 9, 5, 4, 5, 7, 9, 6, 4, 5, 6, 4, 4, 8, 8, 8, 6, 2, 8, 3, 0, 1, 1, 0, 6, 5, 5, 3, 4, 1, 9, 6, 1, 8, 9, 1, 0, 0, 7, 1, 1, 9, 0, 8, 7, 7, 5, 6, 0, 3, 0, 5, 0, 5, 1, 3, 1, 7, 2, 7, 8, 4, 5, 7, 5, 9, 2, 4, 7, 3, 3, 2, 3, 7, 8, 4, 6, 3, 5, 1, 2, 0, 8, 8, 3, 7, 9, 3, 2, 2, 4, 8, 9, 6
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Not equal to exp(-4/9), which agrees with the first 16 decimal places. Related to Jacobi theta constant theta_2 and Dedekind's eta(x^2)^2/eta(x): Sum_{n>=0} x^(n*(n+1)/2) = 1.9873697... (A106334). This constant divided by constant A106334 equals constant A106335, the radius of convergence of the g.f. of A106336.
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FORMULA
| Sum_{n>=0} (1 - n*(n+1)/2)*x^(n*(n+1)/2) = 0.
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EXAMPLE
| 0 = 1 - 2*x^3 - 5*x^6 - 9*x^10 - 14*x^15 - 20*x^21 - 27*x^28 - ...
x=0.641180388429954579645644888628301106553419618910071190877560305051317278
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PROG
| (PARI) solve(x=.6, .7, sum(n=0, 100, (1-n*(n+1)/2)*x^(n*(n+1)/2)))
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CROSSREFS
| Cf. A106334, A106335, A106332, A106336.
Sequence in context: A021160 A060780 A199391 * A104748 A117335 A021863
Adjacent sequences: A106330 A106331 A106332 * A106334 A106335 A106336
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KEYWORD
| cons,nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 29 2005
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