Talk:Airy function

message: Hi,
I should say that in the integral formula for the Bi Airy function the exponential expression misses the zt component.
See eg Abramowitz formula 10.4.33.
regards, jan
:Checked and fixed, thanks. -- Jitse Niesen 12:45, 25 Feb 2004 (UTC)
thread_title: Untitled

message: the asymptotic formula for Ai and Bi when x sto -infinite seems to be inverted 
regards
:You're right. Thanks very much for letting us know. -- Jitse Niesen (talk) 13:17, 5 October 2006 (UTC)
thread_title:  Asymptotic formula 

message: One should write down two ways to solve the Airy equation:
1. The series solution method and,
2. The Laplace transform.
With regard to the Laplace transform, one should explain how to take the contour on the complex plane.
Watson1905 (talk) 20:50, 11 February 2014 (UTC)
thread_title:  Solving the Airy equation 

message: As far as I can see, both Ai(x) and Bi(x) are convex for positiv x.  Juergen.
:Indeed. The differential equation immediately implies that y>0 if x>0 and y>0. Thanks. -- Jitse Niesen (talk) 00:23, 9 November 2006 (UTC)
thread_title:  Properties 

message: "the asymptotic formula for Ai and Bi when x sto -infinite seems to be inverted"
This is still not quite correct.  If the asymptotic expressions for Ai(x) and
Bi(x) at large negative real x, as given on the Article page, are interchanged, 
then a minus sign needs to be put in front of the new expression for Bi(x).
Alternatively, the given expressions can be corrected without interchanging them:
in the arguments of the sine and cosine terms, one changes the sign of the factor
pi/4 from minus to plus. LROS 13:23, 28 November 2006 (UTC)
replies: text: I don't know what it is; for some reason, this seems to be extremely confusing for me. I changed the sign of pi/4 and I hope everything is correct now, as this is all very embarrassing. -- Jitse Niesen (talk) 07:49, 29 November 2006 (UTC)
thread_title:  Asymptotic formula again 

message: Bi(x) is apparently colloquially known as the "Bairy" function. Unfortunately a Google search gives mainly references to function libraries using the term as an abbreviation, so I don't know how to back it up. Confusing Manifestation 06:15, 24 May 2007 (UTC)
thread_title:  Bairy function 

message: Last night, Arthur Rubin removed a link to an web calculator providing useful free services to users of airy functions. Many wikipedia articles on topics that have calculational aspects provide links to web calculators. This was the only calculator link on the article, so the link to that useful service is now gone. Web calcualtors for such relative obscrure functions are rare. Please cite an official policy justifcation, explain your actions in light of these points, or engage in a conversation as to why you believe this information to be inappropriate. Otherwise I plan to revert the change. Ichbin-dcw (talk) 19:47, 25 May 2010 (UTC)
thread_title:  Web Calculators 

message: This article is a prime example of that set of Wikipedia pages that talks at length about a subject without ever explaining it. rowley (talk) 18:40, 3 June 2010 (UTC)
thread_title:  Everything but what it is 

message: In undergraduate optics classes, it's taught that the Airy function is what's listed on: http://www.phy.davidson.edu/stuhome/cabell_f/diffractionfinal/pages/fabry.htm#Characteristics or http://www.tecoptics.com/etalons/theory.htm .  It would be great to update this page to include this popular equation. OpticalEngineer (talk) 02:56, 31 July 2012 (UTC)
thread_title:  Disambiguation: Fabry-Perot etalon Airy Function 

message: One can define the Airy wavelength \lambda in terms of a far-field distance X and wavenumber k_0 at that distance (such that Ai(x/\lambda) oscillates like \sin (k_0 x + \phi) at x \sim X). Can anyone provide a good reference for this usage?
One should explain the meaning of Airy transform and that it is a unitary transform.
Also one should PROOF the orthogonality of Airy functions. This is quite important in physical problems.  — Preceding unsigned comment added by Watson1905 (talk • contribs) 22:06, 10 February 2014 (UTC)
thread_title:  Airy wavelength 

message: One should explain the meaning of Airy transform and that it is a unitary transform.
Also one should PROOF the orthogonality of Airy functions. This is quite important in physical problems.
Watson1905 (talk) 20:42, 11 February 2014 (UTC)
thread_title:  Orthogonality and unitarity properties

message: Why does the article say “Airy function Ai(x)” or “The function Ai(x) and the related function Bi(x)”? The functions are called “Ai” and “Bi” respectively, “(x)” is the function application at x and not the function itself anymore. 1234qwer1234qwer4 (talk) 14:07, 1 November 2019 (UTC)
thread_title:  Ai(x)