A lot of apparently innocent elementary functions, like exp(-x^2) or (sin x)/x, have not antiderivatives in terms of elementary functions. I've read that "Differential Galois theory" explains this, and gives an algorithmic method to know if a given elementary function has or has not elementary antiderivative.(adsbygoogle = window.adsbygoogle || []).push({});

Please, can you explain to me the fundamental, core ideas of this theory?. Some practical, as elementary as possible references? Examples of its use?. Thank you, kowalski.

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

Dismiss Notice

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!

# Differential Galois Theory: exp(-x^2) has no elementary antiderivative

Loading...

Similar Threads for Differential Galois Theory | Date |
---|---|

B What's the difference between 1000e^0.05t and 1000*1.05^t? | Yesterday at 6:18 AM |

A Runge Kutta finite difference of differential equations | Mar 19, 2018 |

I How to find a solution to this linear ODE? | Feb 21, 2018 |

A How to simplify the solution of the following linear homogeneous ODE? | Feb 18, 2018 |

A Causality in differential equations | Feb 10, 2018 |

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