greetings . we have the integral :(adsbygoogle = window.adsbygoogle || []).push({});

[tex] I(s)=\int_{0}^{\infty}\frac{s(E_{s}(x^{s})-1)-x}{x(e^{x}-1)}dx [/tex]

which is equivalent to

[tex] =I(s)=\frac{1}{4}\int_{0}^{\infty}\frac{\theta(ix)\left(sE_{s/2} ((\pi x)^{s/2})-s-2x^{1/2}\right)}{x}dx [/tex]

[itex]E_{\alpha}(z)[/itex] being the mittag-leffler function

and [itex] \theta(x) [/itex] is the jacobi theta function

the integral above behaves well for Re(s)>1 . i am trying to extend the domain of [itex]I(s)[/itex] to the whole complex plane except for some points. but i have no idea where to start !!

**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!

# Analytic continuation of an integral involving the mittag-leffler function

Loading...

Similar Threads - Analytic continuation integral | Date |
---|---|

Contour integration & the residue theorem | Sep 1, 2015 |

Analytical continuation by contour rotation | Jun 4, 2015 |

Analytic continuation of Airy function | May 19, 2015 |

Analytic continuation and physics | May 10, 2015 |

Extending radius of convergence by analytic continuation | Mar 1, 2012 |

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