Timeline for Looking for a "cute" justification for a Catalan-type generating function
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 4, 2020 at 16:12 | answer | added | Johann Cigler | timeline score: 3 | |
| Feb 1, 2020 at 5:08 | answer | added | Max Alekseyev | timeline score: 4 | |
| Jan 31, 2020 at 13:06 | comment | added | esg | Another routine proof: observe that ${1 \over \sqrt{1-4x}}=(x\,C(x))^\prime $, and use Bürmann-Lagrange. | |
| Jan 29, 2020 at 22:52 | comment | added | Fedor Petrov | it is straightforward to get a differential equation of order 2 for the RHS (based on ${a+2n\choose n}(a+n)=(a+2n-1)(a+2n){a+2(n-1)\choose n-1}$) and check that LHS satisfies it and appropriate initial conditions. Not very clever, but quite a universal method. | |
| Jan 29, 2020 at 21:42 | comment | added | Max Alekseyev | It's known that $$c(x)^a = \sum_n \frac{a}{a+2n}\binom{a+2n}{n}x^n.$$ | |
| Jan 29, 2020 at 19:13 | answer | added | Marcus M | timeline score: 10 | |
| Jan 29, 2020 at 16:13 | comment | added | T. Amdeberhan | Please provide some "cute" or "clever" proof. | |
| Jan 29, 2020 at 16:07 | comment | added | Nemo | You should consult known textbooks before asking a question dlmf.nist.gov/15.4.E18 | |
| Jan 29, 2020 at 15:55 | history | asked | T. Amdeberhan | CC BY-SA 4.0 |