The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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