erfcx_derivative()

double stan::math::opencl_kernels::erfcx_derivative	(	double	x,
		double	value
	)

Derivative of erfcx, 2 * x * erfcx(x) - 2 / sqrt(pi).

That difference cancels for large x: both terms approach 2 / sqrt(pi) while the result decays like 1 / (sqrt(pi) * x^2). For x >= 4 the constant cancels analytically against the leading term of the tail rational, leaving 2 * u * C(u). Above 30 it comes from the asymptotic expansion of -sqrt(pi) * x^2 * erfcx'(x) in u, whose coefficients satisfy c_{n+1} = -(n + 3/2) * c_n.

Takes the value as an argument so the reverse pass does not evaluate erfcx twice.

Parameters

x	argument
value	erfcx(x)

Returns

derivative of erfcx at x

Definition at line 76 of file erfcx.hpp.