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

I came across a somewhat unwieldy sum which I do not know how to manipulate any further. I suspect it might have something to do with a hypergeometric series, but I am not sufficiently familar with those series to be able to just see how it might be related to them.

The sum in question is

[tex]\sum_{1\leq r_1< r_2 < \dots < r_n \leq m}{\frac{ (k-1)!!(k-2r_1)!!(k-2r_2+1)!! \dots (k-2r_{n-1}+n-2)!!(k-2r_n+n-1)!! }{ (k-2r_1+1)!!(k-2r_2+2)!! \dots (k-2r_{n-1}+n-1)!!(k-2r_n+n)!! }}[/tex]

where k is some non-negative integer, [tex]0\leq n \leq k[/tex]. m is defined by

[tex]m=\left\lfloor\frac{k+n}{2}\right\rfloor \geq n[/tex].

Do you know of any books where I could look up things like that?

Any help is greatly appreciated.

-Pere

**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!

# Value of finite sum

Loading...

Similar Threads - Value finite | Date |
---|---|

I Getting a matrix into row-echelon form, with zero-value pivots | Feb 17, 2018 |

I Regarding the linear dependence of eigenvectors | Mar 1, 2017 |

B Minimum value | Feb 28, 2017 |

I Difference Equation Boundary Conditions0. | Oct 10, 2016 |

I Third Invariant expressed with Cayley-Hamilton Theorem | Apr 11, 2016 |

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