Timeline for Sum of products of binomials
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2018 at 20:37 | comment | added | user64494 | @Simone Melchiorre Chiarello: Hope you know that hypergemetric functions may be converted to elementary functions for certain values of their parameters. | |
| Feb 19, 2018 at 19:29 | comment | added | Simone Melchiorre Chiarello | Dear user64494, I looked at your answer, but I don't consider it very useful. Indeed, checking the definition of hypergeometric functions, this is little more than rewriting the definition. You could write up hypergeometric functions even for other (simpler) identities involving sums of products of binomials, although you might have a simple answer like the one in Vandermonde-Chu identity. I hoped some simple formula existed also for my sum, but apparently it is hopeless. Probably a combinatorial interpretation would be preferrable at this point. | |
| Feb 19, 2018 at 17:59 | comment | added | user64494 | @Simone Melchiorre Chiarello: Are you serious? But you wrote in the question "but rather in an expression that does not involve a summation, like the ones before ". | |
| Feb 19, 2018 at 17:55 | comment | added | Andrey Rukhin | @user64494 "Therefore I am not interested in a "generating function" answer, but rather in an expression that does not involve a summation, like the ones before. " | |
| Feb 19, 2018 at 17:47 | comment | added | user64494 | @Simone Melchiorre Chiarello: Maple and Mathematica derive a closed-form expression for the sum under considerarion. This is a technical stuff. Did you look at my answer before commenting? | |
| Feb 19, 2018 at 17:43 | comment | added | Simone Melchiorre Chiarello | Thank you for answering. It is pretty disappointing, that even for b=0 there is no simple answer for general a. I think this shatters the hope for a closed formula. | |
| Feb 19, 2018 at 16:13 | history | answered | Andrey Rukhin | CC BY-SA 3.0 |