Asymptotic form of imaginary error function
I am interested in the asymptotic form of the imaginary error function for large, real arguments. I find [1] the following:
$$ text{erfi}(z) = -i + frac{e^{z^2}}{sqrtpi}left(z^{-1} + frac12 z^{-3} + dots right) $$
How is that possible? Set $z = x rightarrow infty$ (where $x in mathbb{R}$) which gives at leading order
$$ text{erfi}(x) approx -i + frac{e^{x^2}}{sqrt{pi}x} $$
I read: left-hand side = real number, right-hand side = complex number. How can that be correct?
[1] http://mathworld.wolfram.com/Erfi.html
error-function
asked Nov 20 '18 at 22:56
Jens
316
add a comment |
I am interested in the asymptotic form of the imaginary error function for large, real arguments. I find [1] the following:
$$ text{erfi}(z) = -i + frac{e^{z^2}}{sqrtpi}left(z^{-1} + frac12 z^{-3} + dots right) $$
How is that possible? Set $z = x rightarrow infty$ (where $x in mathbb{R}$) which gives at leading order
$$ text{erfi}(x) approx -i + frac{e^{x^2}}{sqrt{pi}x} $$
I read: left-hand side = real number, right-hand side = complex number. How can that be correct?
[1] http://mathworld.wolfram.com/Erfi.html
error-function
asked Nov 20 '18 at 22:56
Jens
316
add a comment |
I am interested in the asymptotic form of the imaginary error function for large, real arguments. I find [1] the following:
$$ text{erfi}(z) = -i + frac{e^{z^2}}{sqrtpi}left(z^{-1} + frac12 z^{-3} + dots right) $$
How is that possible? Set $z = x rightarrow infty$ (where $x in mathbb{R}$) which gives at leading order
$$ text{erfi}(x) approx -i + frac{e^{x^2}}{sqrt{pi}x} $$
I read: left-hand side = real number, right-hand side = complex number. How can that be correct?
[1] http://mathworld.wolfram.com/Erfi.html
error-function
asked Nov 20 '18 at 22:56
Jens
316
I am interested in the asymptotic form of the imaginary error function for large, real arguments. I find [1] the following:
$$ text{erfi}(z) = -i + frac{e^{z^2}}{sqrtpi}left(z^{-1} + frac12 z^{-3} + dots right) $$
How is that possible? Set $z = x rightarrow infty$ (where $x in mathbb{R}$) which gives at leading order
$$ text{erfi}(x) approx -i + frac{e^{x^2}}{sqrt{pi}x} $$
I read: left-hand side = real number, right-hand side = complex number. How can that be correct?
[1] http://mathworld.wolfram.com/Erfi.html
error-function
error-function
asked Nov 20 '18 at 22:56
Jens
316
asked Nov 20 '18 at 22:56
Jens
316
asked Nov 20 '18 at 22:56
Jens
316
asked Nov 20 '18 at 22:56
Jens
316
asked Nov 20 '18 at 22:56
Jens
316
316
add a comment |
add a comment |
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