A133843 - OEIS

%I #18 Sep 18 2014 04:53:29

%S 1,5,0,1,9,7,5,2,6,8,2,6,8,6,1,1,4,9,8,8,6,0,3,4,8,7,0,8,0,2,9,1,2,2,

%T 5,9,9,7,3,3,8,6,1,9,0,2,1,4,4,6,5,5,1,7,0,6,5,6,8,3,4,7,3,1,0,5,2,9,

%U 7,9,1,0,4,7,3,9,8,5,9,5,3,4,2,9,2,2,8,8,0,0,6,2,7,7,8,1,1,0,4,5,2,5,2,9,8

%N Decimal expansion of the position of the real positive inflection point of Dawson's integral D_+(x).

%H Stanislav Sykora, <a href="/A133843/b133843.txt">Table of n, a(n) for n = 1..2000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DawsonsIntegral.html">Dawson's Integral</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dawson_function">Dawson function</a>

%e 1.5019752682686114988...

%t RealDigits[x /. FindRoot[-2*Sqrt[Pi]*Erfi[x]*x^2 + 2*E^x^2*x + Sqrt[Pi]*Erfi[x], {x, 1}, WorkingPrecision -> 105]][[1]] (* _Jean-François Alcover_, Nov 08 2012 *)

%o (PARI) Erfi(z) = -I*(1.0-erfc(I*z));

%o Dawson(z) = 0.5*sqrt(Pi)*exp(-z*z)*Erfi(z); \\ same as F(x)=D_+(x)

%o D2Dawson(z) = -2.0*(z + (1.0-2.0*z*z)*Dawson(z)); \\ 2nd derivative

%o x = solve(z=1.0, 2.0, real(D2Dawson(z))) \\ _Stanislav Sykora_, Sep 17 2014

%Y Cf. A133841, A133842, A243433, A245262, A247445.

%K nonn,cons

%O 1,2

%A _Eric W. Weisstein_, Sep 26 2007