Turns out the sum is always 1(!). I wasn't able to prove this with sympy though. This ``` import sympy
n = sympy.Symbol('n') r = sympy.Symbol('r') i = sympy.Symbol('i') j = sympy.Symbol('j') s = sympy.Sum(sympy.Sum( (-1)**(i+j) * sympy.binomial(n+r+1, i) * sympy.binomial(n-r, i) * sympy.binomial(n+r+1, j) * sympy.binomial(n-r, j) / sympy.binomial(2*n+1, i+j), (j, 0, n-r)), (i, 0, n-r)) ``` isn't very cooperative with `doit()`. On Thu, Nov 23, 2017 at 8:15 PM Aaron Meurer <asmeu...@gmail.com> wrote: > You can try using combsimp(). I think it has also received some > improvements in master. > > You can also try using SymPy to evaluate the sum. > > Aaron Meurer > > On Thu, Nov 23, 2017 at 2:43 AM, Nico Schlömer <nico.schloe...@gmail.com> > wrote: > >> Given natural numbers n, r, 0<=r<=n, I'm dealing with the expression >> >> >> <https://lh3.googleusercontent.com/-hhIypvImNS4/WhaYAHKyE4I/AAAAAAABNUk/wBJbs4K02j0ftJtmWvD8uEKggygSn7VHACLcBGAs/s1600/sums.png> >> >> >> I have the strong suspicion that this can be simplified to a product of >> binomial coefficients. Is there any way that sympy can help me here? >> > -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sympy+unsubscr...@googlegroups.com. > > >> To post to this group, send email to sympy@googlegroups.com. >> Visit this group at https://groups.google.com/group/sympy. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/4bc2df75-3944-4e69-abe2-eada30c3fc64%40googlegroups.com >> <https://groups.google.com/d/msgid/sympy/4bc2df75-3944-4e69-abe2-eada30c3fc64%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> For more options, visit https://groups.google.com/d/optout. >> > -- > You received this message because you are subscribed to a topic in the > Google Groups "sympy" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sympy/J2pjEQZnSsc/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAKgW%3D6LnJ5YsVt1LhHbdgZ5nTqsrO2KX17j36OrR2-F8PjcSXg%40mail.gmail.com > <https://groups.google.com/d/msgid/sympy/CAKgW%3D6LnJ5YsVt1LhHbdgZ5nTqsrO2KX17j36OrR2-F8PjcSXg%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAK6Z60fF_0aGAfEkN6P-FH7fD62Q5ap6cfrHZTKxTPtNVmNcjg%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.