login
A247445
Decimal expansion of the negative derivative of Dawson integral at its inflection points.
3
2, 8, 4, 7, 4, 9, 4, 3, 9, 6, 5, 6, 8, 4, 6, 4, 8, 2, 5, 2, 2, 0, 3, 1, 5, 7, 4, 4, 6, 7, 7, 3, 4, 1, 7, 4, 5, 4, 6, 6, 2, 5, 5, 2, 7, 7, 0, 6, 2, 8, 4, 7, 4, 1, 6, 8, 7, 6, 0, 7, 5, 9, 5, 1, 7, 0, 2, 6, 8, 3, 1, 7, 3, 2, 0, 4, 7, 8, 4, 5, 8, 6, 3, 7, 3, 7, 5, 4, 5, 8, 1, 7, 9, 4, 6, 3, 4, 2, 4, 1, 2, 4, 9, 7, 1
OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Dawson's Integral
Wikipedia, Dawson function
FORMULA
Equals 1/(2*xinfl^2-1) = A245262/xinfl, where xinfl=A133843.
EXAMPLE
0.284749439656846482522031574467734174546625527706284741687607595170...
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)
DDawson(z) = 1.0 - 2*z*Dawson(z); \\ 1st derivative of the above
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 = -DDawson(xinfl);
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Sep 17 2014
STATUS
approved