QI (F series): Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Shuipzv3
en>Deoli1
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
In mathematics, a '''Lamé function''' (or '''ellipsoidal harmonic function''') is a solution of '''Lamé's equation''', a second-order [[ordinary differential equation]].  It was introduced in the paper {{harvs|first=Gabriel|last= Lamé|authorlink= Gabriel Lamé|year=1837}}. Lamé's equation appears in the method of [[separation of variables]] applied to the [[Laplace equation]] in [[elliptic coordinates]]. In some special cases solutions can be expressed in terms of polynomials called '''Lamé polynomials'''.


Lamé functions are discussed in detail in {{harvs|loc=Chapter XV | last1=Erdélyi | first1=Arthur | last2=Magnus | first2=Wilhelm | author2-link=Wilhelm Magnus | last3=Oberhettinger | first3=Fritz | last4=Tricomi | first4=Francesco G. | title=Higher transcendental functions. Vol. III | publisher=McGraw–Hill Book Company, Inc., New York-Toronto-London | mr=0066496 | year=1955}}


Lamé's equation is  
By investing in a premium Word - Press theme, you're investing in the future of your website. It is thus, on these grounds that compel various web service provider companies to integrate the same in their packages too. * A community forum for debate of the product together with some other customers in the comments spot. 2- Ask for the designs and graphics that will be provided along with the Word - Press theme. The number of options offered here is overwhelming, but once I took the time to begin to review the video training, I was amazed at how easy it was to create a squeeze page and a membership site. <br><br>The Internet is a vast open market where businesses and consumers congregate. Wordpress have every reason with it which promote wordpress development. This is the reason for the increased risk of Down Syndrome babies in women over age 35.  If you have any kind of inquiries relating to where and exactly how to make use of [http://dinky.in/?WordpressBackupPlugin8334 backup plugin], you can contact us at our website. So if you want to create blogs or have a website for your business or for personal reasons, you can take advantage of free Word - Press installation to get started. As soon as you start developing your Word - Press MLM website you'll see how straightforward and simple it is to create an online presence for you and the products and services you offer. <br><br>ve labored so hard to publish and put up on their website. The nominee in each category with the most votes was crowned the 2010 Parents Picks Awards WINNER and has been established as the best product, tip or place in that category. Are you considering getting your website redesigned. Storing write-ups in advance would have to be neccessary with the auto blogs. Purchase these from our site, or bring your own, it doesn't matter, we will still give you free installation and configuration. <br><br>The next thing I did after installing Wordpress was to find myself a free good-looking Wordpress-theme offering the functionality I was after. But the Joomla was created as the CMS over years of hard work. Normally, the Word - Press developers make a thorough research on your website goals and then ingrain the most suitable graphical design elements to your website. A whole lot worse, your site will likely be useless as well as your merchandise won't sell if no one has the endurance to wait for the web pages to load. Word - Press offers constant updated services and products, that too, absolutely free of cost. <br><br>As a open source platform Wordpress offers distinctive ready to use themes for free along with custom theme support and easy customization. As a website owner, you can easily manage CMS-based website in a pretty easy and convenient style. In simple words, this step can be interpreted as the planning phase of entire PSD to wordpress conversion process. It is a fact that Smartphone using online customers do not waste much of their time in struggling with drop down menus. Likewise, professional publishers with a multi author and editor setup often find that Word - Press lack basic user and role management capabilities.
:<math>\frac{d^2y}{dx^2} = (A+B\weierp(x))y</math>
where ''A'' and ''B'' are constants, and <math>\wp</math> is the [[Weierstrass elliptic function]].  
The most important case is when  ''B'' is of the form ''n''(''n''&nbsp;+&nbsp;1) for an integer ''n'', in which case the solutions extend to meromorphic functions defined in the whole complex plane. For other values of ''B'' the solutions have [[branch point]]s.
 
By changing the independent variable, Lamé's equation can also be rewritten in algebraic form as
:<math>\frac{d^2y}{dt^2} +\frac{1}{2}\left(\frac{1}{t-e_1}+\frac{1}{t-e_2}+\frac{1}{t-e_3}\right)\frac{dy}{dt} = \frac{A+Bt}{4(t-e_1)(t-e_2)(t-e_3)}y</math>
which after a change of variable becomes a special case of [[Heun's equation]].
 
==References==
 
*{{Citation
| last = Erdélyi
| first = Arthur
| authorlink = Arthur Erdélyi
| last2 = Magnus
| first2 = Wilhelm
| author2-link = Wilhelm Magnus
| last3 = Oberhettinger
| first3 = Fritz
| last4 = Tricomi
| first4 = Francesco G.  
| author4-link = Francesco Tricomi
| title = Higher transcendental functions
| series = Bateman Manuscript Project
| volume = Vol. III
| place = New York–Toronto–London
| publisher = [[McGraw-Hill]]
| pages = XVII + 292
| year = 1955
| url = http://apps.nrbook.com/bateman/Vol3.pdf
| mr = 0066496
| zbl = 0064.06302
}}.
*{{Citation
| first = G.
| last = Lamé
| author-link = Gabriel Lamé
| title = Sur les surfaces isothermes dans les corps homogènes en équilibre de température
| journal = [[Journal de mathématiques pures et appliquées]] 
| volume = 2 
| year = 1837
| pages = 147–188
| url = http://gallica.bnf.fr/ark:/12148/bpt6k163818/f155.image
}}. Available at [[Gallica]].
*{{springer|id=L/l057400|first=N. Kh.|last= Rozov|title=Lamé equation}}
*{{springer|id=L/l057410|first=N. Kh.|last= Rozov|title=Lamé function}}
*{{dlmf|id=29|first=H. |last=Volkmer}}
 
{{DEFAULTSORT:Lame function}}
[[Category:Special functions]]

Latest revision as of 18:19, 1 November 2014


By investing in a premium Word - Press theme, you're investing in the future of your website. It is thus, on these grounds that compel various web service provider companies to integrate the same in their packages too. * A community forum for debate of the product together with some other customers in the comments spot. 2- Ask for the designs and graphics that will be provided along with the Word - Press theme. The number of options offered here is overwhelming, but once I took the time to begin to review the video training, I was amazed at how easy it was to create a squeeze page and a membership site.

The Internet is a vast open market where businesses and consumers congregate. Wordpress have every reason with it which promote wordpress development. This is the reason for the increased risk of Down Syndrome babies in women over age 35. If you have any kind of inquiries relating to where and exactly how to make use of backup plugin, you can contact us at our website. So if you want to create blogs or have a website for your business or for personal reasons, you can take advantage of free Word - Press installation to get started. As soon as you start developing your Word - Press MLM website you'll see how straightforward and simple it is to create an online presence for you and the products and services you offer.

ve labored so hard to publish and put up on their website. The nominee in each category with the most votes was crowned the 2010 Parents Picks Awards WINNER and has been established as the best product, tip or place in that category. Are you considering getting your website redesigned. Storing write-ups in advance would have to be neccessary with the auto blogs. Purchase these from our site, or bring your own, it doesn't matter, we will still give you free installation and configuration.

The next thing I did after installing Wordpress was to find myself a free good-looking Wordpress-theme offering the functionality I was after. But the Joomla was created as the CMS over years of hard work. Normally, the Word - Press developers make a thorough research on your website goals and then ingrain the most suitable graphical design elements to your website. A whole lot worse, your site will likely be useless as well as your merchandise won't sell if no one has the endurance to wait for the web pages to load. Word - Press offers constant updated services and products, that too, absolutely free of cost.

As a open source platform Wordpress offers distinctive ready to use themes for free along with custom theme support and easy customization. As a website owner, you can easily manage CMS-based website in a pretty easy and convenient style. In simple words, this step can be interpreted as the planning phase of entire PSD to wordpress conversion process. It is a fact that Smartphone using online customers do not waste much of their time in struggling with drop down menus. Likewise, professional publishers with a multi author and editor setup often find that Word - Press lack basic user and role management capabilities.