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A243433 Decimal expansion of c = twice the maximum of Dawson's integral, a constant used in the asymptotic evaluation of the ideal hyperbolic n-cube volume. 6
1, 0, 8, 2, 0, 8, 8, 4, 4, 9, 2, 7, 0, 3, 6, 3, 3, 9, 6, 9, 4, 5, 5, 1, 8, 6, 6, 0, 4, 8, 2, 9, 5, 4, 3, 7, 2, 7, 8, 1, 2, 0, 9, 3, 5, 3, 6, 5, 3, 6, 5, 1, 7, 7, 4, 9, 1, 2, 7, 0, 8, 4, 3, 3, 8, 1, 6, 8, 4, 1, 1, 1, 7, 5, 9, 6, 2, 9, 3, 9, 5, 0, 6, 2, 8, 7, 8, 3, 8, 2, 0, 4, 2, 6, 4, 5, 5, 5, 4, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Equals the inverse of the position xm of the Dawson integral maximum, and also the negative of the second derivative of the Dawson integral at xm. - Stanislav Sykora, Sep 17 2014
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.9 Hyperbolic volume constants, p. 512.
LINKS
Eric Weisstein's MathWorld, Dawson's Integral
Wikipedia, Dawson function
FORMULA
Volume(n) ~ 2*sqrt(Pi)*c^n/GAMMA((n+1)/2), where GAMMA is the Euler gamma function.
Equals 1/A133841 = 2*A133842.- Stanislav Sykora, Sep 17 2014
EXAMPLE
1.0820884492703633969455186604829543727812...
MATHEMATICA
digits = 100; DawsonF[x_] := Sqrt[Pi]*Erfi[x]/(2*Exp[x^2]); c = 2*DawsonF[x] /. FindRoot[DawsonF'[x], {x, 1}, WorkingPrecision -> digits+5]; RealDigits[c, 10, digits] // First
PROG
(PARI) Erfi(z) = -I*(1.0-erfc(I*z));
Dawson(z) = 0.5*sqrt(Pi)*exp(-z*z)*Erfi(z);
DDawson(z) = 1.0 - 2*z*Dawson(z); \\ Derivative of the above
x = 1.0/solve(z=0.1, 2.0, real(DDawson(z))) \\ Stanislav Sykora, Sep 17 2014
CROSSREFS
Sequence in context: A011105 A098829 A190404 * A080729 A262080 A164800
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified June 16 19:52 EDT 2024. Contains 373432 sequences. (Running on oeis4.)