A245262 - OEIS

A245262

Decimal expansion of Dawson's integral at the inflection point.

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

0,1

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 = 0..2000

Eric Weisstein's MathWorld, Dawson's Integral

Wikipedia, Dawson function

FORMULA

Equals xinfl/(2*xinfl^2-1), xinfl = A133843. - Stanislav Sykora, Sep 17 2014

EXAMPLE

0.427686616017928797406755642112695191936245534527819588763606097190352...

MATHEMATICA

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

PROG

(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)));

x = Dawson(xinfl) \\ Stanislav Sykora, Sep 17 2014

CROSSREFS

Cf. A133841, A133842, A133843, A247445.

Sequence in context: A307869 A016695 A125271 * A092314 A237750 A372860

Adjacent sequences: A245259 A245260 A245261 * A245263 A245264 A245265

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Jul 15 2014

STATUS

approved