Timeline for How does Mathematica calculate LaguerreL
Current License: CC BY-SA 3.0
11 events
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| Aug 12, 2015 at 2:00 | vote | accept | Menzel Wang | ||
| Aug 9, 2015 at 3:05 | comment | added | Bob Hanlon |
@MenzelWang - Re: LaguerreL[-1, -1, x] see EDIT 2 in the answer.
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| Aug 9, 2015 at 3:01 | history | edited | Bob Hanlon | CC BY-SA 3.0 |
Added information on evaluation of `LaguerreL[-1, -1, x]`
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| Aug 9, 2015 at 1:27 | comment | added | Menzel Wang | Thanks a lot! But I still have a question: run the following codes in Mathematica n = -1 a = -1 LaguerreL[n, a, x] // FunctionExpand Gamma[a + n + 1]/Gamma[n + 1] Hypergeometric1F1Regularized[-n, a + 1, x] // FunctionExpand You will find that the LaguerreL turns out to be -x*Exp[x], but the latter function is not convergent. In this condition, how does Mathematica calculate LaguerreL? | |
| Aug 8, 2015 at 23:53 | history | edited | J. M.'s missing motivation♦ | CC BY-SA 3.0 |
deleted 6 characters in body
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| Aug 8, 2015 at 22:28 | comment | added | Jens |
To simplify even further, you can replace the Pochhammer symbol by Binomial[a + n, n].
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| Aug 8, 2015 at 16:52 | comment | added | ilian |
@Pickett Oh, I see now, it also has a few top level definitions attached related to Series.
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| Aug 8, 2015 at 16:48 | history | edited | Bob Hanlon | CC BY-SA 3.0 |
Added definition using Hypergeometric1F1Regularized bas4d on comment by @ilian
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| Aug 8, 2015 at 16:37 | comment | added | ilian |
@Pickett I am surprised PrintDefinitions would give anything since the implementation is in C and not top level. +1 from me too, I believe the general case is computed in terms of Gamma/Pochhammer and Hypergeometric1F1Regularized as in this definition
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| Aug 8, 2015 at 16:31 | comment | added | C. E.♦ |
Correct, you can also see it by evaluating Needs["GeneralUtilities`"]; PrintDefinitions[LaguerreL] +1
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| Aug 8, 2015 at 16:26 | history | answered | Bob Hanlon | CC BY-SA 3.0 |