I need to approximate this expression in order to sum it. Asymptotically I obtain $\frac1{\sqrt{\pi}x}+\frac1{2\sqrt{\pi} x^2} + O\left(\frac1{x^3}\right)$. Although this looks fine there is the following problem:
If $x=a(1-\frac{k}{b})$ with $ a<
I need to approximate this expression in order to sum it. Asymptotically I obtain $\frac1{\sqrt{\pi}x}+\frac1{2\sqrt{\pi} x^2} + O\left(\frac1{x^3}\right)$. Although this looks fine there is the following problem:
If $x=a(1-\frac{k}{b})$ with $ a<
Maple (with MultiSeries) reports this asymptotic for $\mathrm{erfi}(x)$ ... $$ \Biggl(\frac{1}{\sqrt{\pi} x} + \frac{1}{2 \sqrt{\pi} x^{3}} + \frac{3}{4 \sqrt{\pi} x^{5}} + \frac{15}{8 \sqrt{\pi} x^{7}} + O \Bigl(x^{(-8)}\Bigr)\Biggr) \operatorname{e} ^{x^{2}} $$ Maple's definition of erfi is equivalent to: $$ \mathrm{erfi}(x) = \frac{2}{\sqrt{\pi}} \int_{0}^{x} \operatorname{e} ^{s^{2}} d s $$