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.

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

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

Stanislav Sykora, Table of n, a(n) for n = 1..2000

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

Cf. A133841, A133842.

Sequence in context: A011105 A098829 A190404 * A080729 A262080 A164800

Adjacent sequences: A243430 A243431 A243432 * A243434 A243435 A243436

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 05 2014

Status

approved