I there.(adsbygoogle = window.adsbygoogle || []).push({});

I'm currently using this kind of integrals, with n even, and I couldn't found anything in internet for calculate this.

Let

From the book I'm studying Ashcroft/Mermin, Solid State Physics, Append C, it says that

[tex]a_{n}=\int_{-\infty }^{\infty } \frac{x^n

e^x}{\left(e^x+1\right)^2} \, dx[/tex]

can, by elementary operations, be written as

[tex]a_{n}=1+\frac{1}{2^{2n}}+\frac{1}{3^{2n}}-\frac{1}{4^{2n}}+...[/tex] and so can be written with the zeta function:

[tex]a_{n}=(2-\frac{1}{2^{2(n+1)}}) \zeta(2n)[/tex]

and, [tex]\zeta(2n)=2^{2n-1}\frac{\pi^{2n}}{(2n)!}B_{n}[/tex] where B_n are the bernoulli numbers.

Well, aren't any easier way, using integration in complex plane? Can you give me an ideia of where can I find a resolution to this?

Thanks,

littlepig

**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!

# Integration of x^n*e^x/(e^x + 1)^2

Loading...

Similar Threads - Integration x^n*e^x | Date |
---|---|

I Integrate a function over a closed circle-like contour around an arbitrary point on a torus | Yesterday at 12:51 PM |

A Integrate f(x) = tanh(c*x^b)? Wolfram says not possible ... | Mar 11, 2018 |

I Looking for additional material about limits and distributions | Feb 17, 2018 |

I Solving integral | Feb 9, 2018 |

Integral of e^-mod(x^n) | Oct 29, 2009 |

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