Timeline for $n$-th derivative of $\exp\left(-\frac{\lambda(x-\mu)^2}{2\mu^2x}\right)$
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22 at 13:00 | comment | added | Fred Hucht | I expanded the LHS of (1) for $n=3,\ldots,7$ using Mathematica's Apart[] (with the substitution $\lambda \mapsto 2 t x$). The resulting terms, e.g., $5040 - 15120 t + 12600 t^2 - 4200 t^3 + 630 t^4 - 42 t^5 + t^6$ for $n=7$, were looked up and identified as generalized Laguerre polynomials using oeis.org. Finally, the prefactors were adjusted. | |
| Apr 22 at 12:13 | comment | added | NancyBoy | Thank you @Fred Hucht for your answer! Could you be a bit more explicit on the main steps of "some algebra" ? Thank you! | |
| Apr 22 at 9:13 | history | answered | Fred Hucht | CC BY-SA 4.0 |