Timeline for Is there an oscillating analog of the Gaussian distribution?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 25, 2014 at 8:19 | comment | added | F. C. | Oops, I should have said "numerators of $q$-Bernoulli numbers". These rational functions were introduced by Carlitz in Carlitz, L. q-Bernoulli numbers and polynomials. Duke Math. J. 15, (1948). 987–1000. They are available in sage as follows: "from sage.combinat.q_bernoulli import q_bernoulli" then "q_bernoulli(20).numerator()" | |
| Feb 25, 2014 at 0:34 | comment | added | Eckhard | Can you post a reference with more information about these "numerators of q-Bernoulli polynomials"? Google doesn't bring up much. | |
| Feb 24, 2014 at 22:50 | answer | added | Gerald Edgar | timeline score: 5 | |
| Feb 24, 2014 at 22:08 | answer | added | Gerald Edgar | timeline score: 0 | |
| Feb 24, 2014 at 21:56 | comment | added | Eckhard | Nice question. For the record, the scaling that transform the coefficients $(i,c_i)$ of $(1+x)^n$ into a standard normal PDF is given by $(x,y)\mapsto\left((2x-n)/\sqrt{n},\sqrt{n}y/2^{n+1}\right)$. | |
| Feb 24, 2014 at 21:56 | answer | added | Noam D. Elkies | timeline score: 3 | |
| Feb 24, 2014 at 20:20 | comment | added | F. C. | I have now added an image where one can compare the decay with the decay of a similar Gaussian. | |
| Feb 24, 2014 at 20:19 | history | edited | F. C. | CC BY-SA 3.0 |
added one image
|
| Feb 24, 2014 at 19:56 | comment | added | Bill Bradley | Do you have a sense of the rate of decay of the function? | |
| Feb 24, 2014 at 17:40 | answer | added | guest | timeline score: 0 | |
| Feb 24, 2014 at 14:59 | comment | added | F. C. | The polynomials are numerators of $q$-Bernoulli polynomials (and variants of that). | |
| Feb 24, 2014 at 14:55 | comment | added | Ilmari Karonen | Yes, I got that, I was just curious about what the specific family was. | |
| Feb 24, 2014 at 14:54 | comment | added | F. C. | The picture is the plot of the list of coefficients of one polynomial (in a familly of polynomials indexed by the integers). This is essentially a sequence of points, one with coordinates $(i,c_i)$ for each monomial $c_i x^i$. | |
| Feb 24, 2014 at 12:31 | comment | added | Ilmari Karonen | The convergence to a Gaussian that you describe is essentially due to the central limit theorem, so you basically seem to be looking for a non-positive analog of a stable distribution. What is that picture of yours a plot of, anyway? | |
| Feb 24, 2014 at 10:50 | history | asked | F. C. | CC BY-SA 3.0 |