Hi,(adsbygoogle = window.adsbygoogle || []).push({});

this is not a homework and my problem is much bigger for me to give full details here. I came across this integral

[itex]\mathcal{I}(\xi)=\int^{\xi_c}_{\xi}{\rm d}\xi^\prime\exp\left[\sqrt{2}\sigma\,{\rm Erf}^{-1}\left(1-\frac{8\pi}{3}{\xi^\prime}^3\right)\right][/itex]

where Erf[itex]^{-1}[/itex] is the inverse error function and

[itex]\xi_c=\left[\frac{3}{8\pi}\left(1-{\rm Erf}\left(\frac{\sigma^2-\sqrt{2}\sigma\,{\rm Erf^{-1}(2\beta-1)}}{\sqrt{2}\sigma}\right)\right)\right]^{1/3}[/itex]

with [itex]0\le\beta\le1[/itex].

I would like get an analytical approximation but I can't figure out a way to do that, even with software like Mathematica. I tried solving the integral numerically and I find a reliable solution, however, I'm mostly interested in points where [itex]\xi\to\xi_c^-[/itex], and here the inverse error function diverges.

Do you have any ideas on how to approximate this integral?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# How to solve an integral with the Inverse error function

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - solve integral Inverse | Date |
---|---|

I Solving integral | Feb 9, 2018 |

I Understanding an integral | Jan 31, 2018 |

I Solving this integral equation | Nov 3, 2017 |

B How do I solve this integral? | Jun 22, 2017 |

I Solving a definite integral by differentiation under the integral | Mar 23, 2017 |

**Physics Forums - The Fusion of Science and Community**