Talk:Laguerre polynomials

message: Can anyone provide more concrete examples of when the Laguerre polynomials arise in real-life science or engineering applications? 171.64.133.56 22:49, 24 February 2006 (UTC)
replies: text: \int_0^\infty L_{n_1} (x) L_{n_2}(x)..L_{n_r}(x) e^{-x} dx,
for a word with n1 letters X1, n2 letters X2,... nr letters Xr.
PMajer 14:00, 3 May 2007 (UTC)

text: Real life? They are the cornerstone of the Hydrogen_atom#Wavefunction in Quantum mechanics, and likewise the cornerstone of the quantum Phase_space_formulation#Simple_harmonic_oscillator. Laguerres are as basic as life itself, as a result.   Cuzkatzimhut (talk) 23:51, 18 September 2013 (UTC)
thread_title: Applications of Laguerre polynomials

message: Mathias, 20th of June 2011:
I added in the article that physicist do not always use the same definition of the associated Laguerre Polynomials and gave some references. I think this is useful information, since any quantum mechanics student will need this and nowadays will look here and to avoid confusing this should be state here. 
Could someone please put the reference in the buttom of the text. Thank you.   — Preceding unsigned comment added by 150.244.101.168 (talk) 11:21, 20 June 2011 (UTC)
thread_title: Definition of Laguerre polynomials

message: Here, as in many other math-related articles, User:Rea5, and other anonymous IPs (probably a dynamic IP) have been adding references to a book authored by Refaat El Ataar. This is not a notable math book (specially because it was edited in 2006!), so many users have been reverting those reference inclusions. Probably, it's a self-reference.
If you are the user who includes this references, please discuss it here first and explain why you think that book should be listed here. Otherwise, references to Refaat El Ataar books in this article will keep being removed.
--John C PI 14:37, 31 January 2006 (UTC)
thread_title:  Bibliography: Self-references 

message: Guys, the paragraph about Relation to hypergeometric functions, had a mistake. The Pochhamer symbol should have a superscript n, not a subscript. Check Abramovitz ans Stegan. I have edited this.Spastas (talk) 00:54, 26 March 2008 (UTC)
replies: text: Maybe you're missing the fact that there are differing and conflicting conventions on the use of the Pochhammer symbol.  See Pochhammer symbol. Michael Hardy (talk) 15:49, 25 March 2008 (UTC)

text: Michael, you are right. I was missing a lot of facts yesterday. I checked Abramowitz and Stegun again. In chapter 22, there is only a relation between the confluent hypergeometric function and the Laguerre polynomials. I have verified both the relations given in this page and they are correct. The Pochhammer symbol is defined with a subscript and not a superscript as I claimed earlier. I think the proper thing to do here is write the Pochhammer symbol with a subscript as is customary in special functions. As the Wolfram site says, this is an unfortunate notation because it is confusing and that is what confused me. I think it would be better if you changed rather than me. I am not too good at this. Spastas (talk) 00:54, 26 March 2008 (UTC)
thread_title:  Error 

message: Hi. The Abramowitz's reference for the asymptotic behaviour for large n is wrong. If you see Abramowitz formula 13.3.8, has nothing to do with this asymptotics. I've searched in Abramowitz, Szego and Askey books looking for this asymptotics expressions, but I have not found them. Are they correct?
Thank you very much.
* The polynomials' asymptotic behaviour for large n, but fixed \alpha and x>0, is given by 
:L_n^{(\alpha)}(x) \approx \frac{n^{\frac{\alpha}{2}-\frac{1}{4}}}{\sqrt{\pi}} \frac{e^{\frac{x}{2}}}{x^{\frac{\alpha}{2}+\frac{1}{4}}} \cos\left(2 \sqrt{x \left(n+\frac{\alpha+1}{2}\right)}- \frac{\pi}{2}\left(\alpha+\frac{1}{2} \right) \right), and
:L_n^{(\alpha)}(-x) \approx \frac{n^{\frac{\alpha}{2}-\frac{1}{4}}}{2\sqrt{\pi}} \frac{e^{-\frac{x}{2}}}{x^{\frac{\alpha}{2}+\frac{1}{4}}} \exp\left(2 \sqrt{x \left(n+\frac{\alpha+1}{2}\right)} \right).  Abramowitz, p. 506, 13.3.8.  —Preceding unsigned comment added by Ehuertasce (talk • contribs) 18:06, 23 May 2009 (UTC)
thread_title:  Error in the reference "The polynomials' asymptotic behaviour for large n, but fixed α and x > 0, is given by" 

message: An algorithm is given for calculating the generalized Laguerre polynomials. Where does it come from?
Nicolas Bigaouette (talk) 23:29, 14 December 2009 (UTC)
thread_title:  Algorithm source 

message: From observing the first few derivatives of e^{-x}x^n, it is clear that Laguerre polynomials can be expressed as (ignoring the 1/n! normalization)
e^x \frac{d^n}{dx^n} (e^{-x}x^n) = \sum_{k=0}^n \left[ \binom{n}{k} (-x)^{n-k} \frac{n!}{(n-k)!} \right]
This is helpful in expressing polynomials of a higher degree than L_6. Should it be added in? I can't find it in a source anywhere, but it works.. I don't know how WP:OR ties in with math articles..--Dudemanfellabra (talk) 15:30, 24 April 2011 (UTC)
thread_title:  Expressed as a summation of binomial coefficients/falling factorials 

message: As part of an ongoing effort to clean our special functions articles of WP:OR, I plan to be removing uncited information from this article in the next few weeks.  I have tagged some sections that need citations.  When removing the content, I will of course try to reference it myself, but it seems unlikely that I will come up with anything for the vast majority (different authors use different conventions, etc.)  I tagged two sections a few weeks ago.  I am going to tag more of the article and return in a few more weeks to remove those items that haven't been cited.  Sławomir Biały (talk) 12:16, 10 October 2011 (UTC)
thread_title:  [[WP:OR]] cleanup 

message: A Google books link for Modern Quantum Mechanics by J.J. Sakurai is . Could someone familiar with this type of reference clean up the citations? Puzl bustr (talk) 19:24, 4 March 2012 (UTC)
thread_title:  References 

message: I found a typo in section 3.3 of the article, in the formula immediately after the line "They can be used to derive the four 3-point-rules"
The expression on the right hand side of the equation depends on the variable k, but there is no k on the left hand side.  I am assuming that this should be an 'n' on the right instead of a 'k'.
128.132.1.254 (talk) 16:28, 14 March 2016 (UTC)
thread_title:  Typo