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

I would like to show directly,

[tex]\int \frac{e^{at}}{e^{it}+e^{-it}}dt=\frac{e^{(i+a) t} \text{Hypergeometric2F1}\left[1,\frac{1}{2}-\frac{i a}{2},\frac{3}{2}-\frac{i a}{2},-e^{2 i t}\right]}{i+a}[/tex]

I realize I can differentiate the antiderivative to show the relation but was wondering how to integrate the integral directly to obtain the hypergeometric function or are these type integrals evaluated using a different technique? I can express it as:

[tex]\int \frac{e^{(i-a)t}}{1+e^{2it}}dt[/tex]

and at least it has the [itex]e^{2it}[/itex] in there.

How are any integrals expressed in terms of hypergeometric functions?

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

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

# How to show integral equal to hypergeometric function?

Loading...

Similar Threads - show integral equal | Date |
---|---|

Showing why an integral is the area under a curve | Sep 6, 2013 |

Showing the properties of differentiating an integral | Jan 18, 2013 |

How to show integral identity involving gaussian over x | Jan 25, 2012 |

To show that an integral is divergent | Oct 8, 2011 |

Show integral is equal to Bessel function | Sep 13, 2011 |

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