A347901 Decimal expansion of a constant related to the asymptotics of A005169.
5, 7, 6, 1, 4, 8, 7, 6, 9, 1, 4, 2, 7, 5, 6, 6, 0, 2, 2, 9, 7, 8, 6, 8, 5, 7, 3, 7, 1, 9, 9, 3, 8, 7, 8, 2, 3, 5, 4, 7, 2, 4, 6, 6, 3, 1, 1, 8, 9, 7, 4, 4, 6, 8, 6, 8, 5, 1, 5, 6, 5, 3, 4, 3, 1, 9, 4, 6, 8, 2, 2, 9, 3, 7, 4, 9, 9, 2, 4, 0, 2, 0, 0, 3, 9, 0, 7, 4, 2, 2, 0, 9, 9, 3, 2, 9, 5, 5, 0, 8, 5, 0, 0, 9, 6, 6
Offset: 0
Examples
0.576148769142756602297868573719938782354724663118974468685156534319...
References
- Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 381.
Links
- A. M. Odlyzko and H. S. Wilf, The editor's corner: n coins in a fountain, Amer. Math. Monthly, 95 (1988), 840-843.
Programs
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Mathematica
FindRoot[Sum[(-1)^k*r^(k^2)/QPochhammer[r, r, k], {k, 0, 1000}] == 0, {r, 1/2}, WorkingPrecision -> 120]
Formula
Lowest root of the equation Sum_{k>=0} (-1)^k * r^(k^2) / QPochhammer(r, r, k) = 0.