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A245262
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Decimal expansion of Dawson's integral at the inflection point.
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3
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4, 2, 7, 6, 8, 6, 6, 1, 6, 0, 1, 7, 9, 2, 8, 7, 9, 7, 4, 0, 6, 7, 5, 5, 6, 4, 2, 1, 1, 2, 6, 9, 5, 1, 9, 1, 9, 3, 6, 2, 4, 5, 5, 3, 4, 5, 2, 7, 8, 1, 9, 5, 8, 8, 7, 6, 3, 6, 0, 6, 0, 9, 7, 1, 9, 0, 3, 5, 2, 0, 5, 5, 9, 0, 8, 8, 3, 4, 0, 0, 3, 6, 9, 6, 4, 3, 9, 6, 9, 8, 3, 4, 2, 8, 4, 5, 8, 8, 9, 3, 4, 9, 1, 6
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.9 Hyperbolic volume constants, p. 512.
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LINKS
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FORMULA
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EXAMPLE
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0.427686616017928797406755642112695191936245534527819588763606097190352...
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MATHEMATICA
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digits = 104; DawsonF[x_] := Sqrt[Pi]*Erfi[x]/(2*Exp[x^2]); xi = x /. FindRoot[DawsonF''[x], {x, 3/2}, WorkingPrecision -> digits + 10]; RealDigits[DawsonF[xi], 10, digits] // First
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PROG
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(PARI) Erfi(z) = -I*(1.0-erfc(I*z));
Dawson(z) = 0.5*sqrt(Pi)*exp(-z*z)*Erfi(z); \\ same as F(x)=D_+(x) D2Dawson(z) = -2.0*(z + (1.0-2.0*z*z)*Dawson(z)); \\ 2nd derivative
xinfl = solve(z=1.0, 2.0, real(D2Dawson(z)));
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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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