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A133842 Decimal expansion of value of the maximum of Dawson's integral D_+(x). 7

%I

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

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

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

%N Decimal expansion of value of the maximum of Dawson's integral D_+(x).

%H Stanislav Sykora, <a href="/A133842/b133842.txt">Table of n, a(n) for n = 0..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>

%F Equals 1/(2*A133841), since F'(x)=1-2*x*F(x). - _Stanislav Sykora_, Sep 17 2014

%e 0.54104422463518169847...

%t DawsonF[x_] := Sqrt[Pi]*Erfi[x]/(2*Exp[x^2]); y0 = DawsonF[x] /. FindRoot[ DawsonF'[x], {x, 1}, WorkingPrecision -> 110]; RealDigits[y0][[1]][[1 ;; 105]] (* _Jean-Fran├žois Alcover_, Oct 26 2012, after _Eric W. Weisstein_ *)

%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 DDawson(z) = 1.0 - 2*z*Dawson(z); \\ Derivative of the above

%o x = 0.5/solve(z=0.1, 2.0, real(DDawson(z))) \\ _Stanislav Sykora_, Sep 17 2014

%Y Cf. A133841, A133843, A243433.

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Sep 26 2007

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)