Timeline for Integral involving Laguerre polynomial
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| S Sep 22, 2022 at 11:27 | history | suggested | tripleee | CC BY-SA 4.0 |
Typo: Fix alot
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| Sep 22, 2022 at 10:53 | review | Suggested edits | |||
| S Sep 22, 2022 at 11:27 | |||||
| Dec 19, 2011 at 23:21 | comment | added | Noam D. Elkies | What are you trying to do with these integrals? For many purposes a generating function is good enough, and here the generating function $\sum_{n=0}^\infty L_n(x) z^n = (z-1)^{-1} \exp(-xz/(z-1))$ yields a closed form for the generating function of your integrals, which is $$ \sqrt{\frac{2\pi}{(z-1)(3z-1)}} \phantom. \exp\left(-\frac{(\alpha^2+6\beta^2)z^2-2(\alpha^2+\beta^2)z + \alpha^2}{2(z-1)(3z-1)}\right) $$ if I calculated (and TeXed) correctly. | |
| Dec 19, 2011 at 23:00 | comment | added | Mark M | Yes, it reports that if you keep $n$ as a parameter... however, if you plug in specific values of $n$ like 0,1,2,3,4,..., you get a well-defined answer. | |
| Dec 19, 2011 at 21:28 | comment | added | Igor Rivin | Interestingly, mathematica keeps telling me that the integral diverges! (even when I change the integral to the integral from $0$ to $\infty,$ and replace your $e^{i a x}$ by $\cos(a x).$ Weird. | |
| Dec 19, 2011 at 18:58 | history | edited | Mark M | CC BY-SA 3.0 |
added 164 characters in body
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| Dec 19, 2011 at 18:43 | history | asked | Mark M | CC BY-SA 3.0 |