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	~~In [[numerical analysis]] '''Gauss–Laguerre quadrature''' is an extension of [[Gaussian quadrature]] method for approximating the value of integrals of the following kind:~~

	~~:<math>\int_{0}^{+\infty} e^{-x} f(x)\,dx.</math>~~

	~~In this case~~		Next - GEN Gallery is a full incorporated Image Gallery plugin for Word - Press which has a Flash slideshow option. Good luck on continue learning how to make a wordpress website. PSD files are incompatible to browsers and are suppose to be converted into wordpress compatible files so that it opens up in browser. Out of the various designs of photography identified these days, sports photography is preferred most, probably for the enjoyment and enjoyment associated with it. The top 4 reasons to use Business Word - Press Themes for a business website are:. <br><br>Any business enterprise that is certainly worth its name should really shell out a good deal in making sure that they have the most effective website that provides related info to its prospect. You do not catch a user's attention through big and large pictures that usually takes a millennium to load up. Well Managed Administration The Word - Press can easily absorb the high numbers of traffic by controlling the server load to make sure that the site works properly. Apart from these, you are also required to give some backlinks on other sites as well. You can also get a free keyword tool that is to determine how strong other competing sites are and number of the searches on the most popular search sites. <br><br>Here are a few reasons as to why people prefer Word - Press over other software's. Now if we talk about them one by one then -wordpress blog customization means customization of your blog such as installation of wordpress on your server by wordpress developer which will help you to acquire the SEO friendly blog application integrated with your site design as well as separate blog administration panel for starting up your own business blog,which demands a experienced wordpress designer. If you have any type of inquiries pertaining to where and how you can make use of [http://miu.tw/wordpress_dropbox_backup_865538 backup plugin], you can contact us at our own website. Are you considering getting your website redesigned. Our skilled expertise, skillfulness and excellence have been well known all across the world. Purchase these from our site, or bring your own, it doesn't matter, we will still give you free installation and configuration. <br><br>Digg Digg Social Sharing - This plugin that is accountable for the floating social icon located at the left aspect corner of just about every submit. This plugin allows a webmaster to create complex layouts without having to waste so much time with short codes. re creating a Word - Press design yourself, the good news is there are tons of Word - Press themes to choose from. If you are looking for Hire Wordpress Developer then just get in touch with him. It does take time to come up having a website that gives you the much needed results hence the web developer must be ready to help you along the route. <br><br>Every single module contains published data and guidelines, usually a lot more than 1 video, and when pertinent, incentive links and PDF files to assist you out. An ease of use which pertains to both internet site back-end and front-end users alike. As a result, it is really crucial to just take aid of some experience when searching for superior quality totally free Word - Press themes, Word - Press Premium Themes for your web site. ) Remote Login: With the process of PSD to Wordpress conversion comes the advantage of flexibility. For your information, it is an open source web content management system.

	~~:<math>\int_{0}^{+\infty} e^{~~-~~x} f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i)</math>~~

	~~where ''x''<sub>''i''</sub>~~ is ~~the ''i''~~-~~th root of [[Laguerre polynomial]] ''L''<sub>''n''</sub>(''x'') and the weight ''w''<sub>''i''</sub> is given by~~
	~~<ref name="AS">[[Milton Abramowitz\|Abramowitz, M~~.~~]] & [[Irene Stegun\|Stegun, I~~. A.]], ~~''Handbook of Mathematical Functions''~~, ~~10th printing~~ with ~~corrections (1972), Dover, ISBN 978-0-486-61272-0. Equation 25~~.4~~.45.[http://www.nrbook.com/abramowitz_and_stegun/page_890.htm access online]</ref>~~

	:~~<math>w_i = \frac {x_i} {(n+1)^2[L_{n+1}(x_i)]^2}~~.<~~/math~~>

	~~==For more general functions==~~

	~~To integrate the function~~ <~~math~~>~~f</math> we apply~~ the ~~following transformation~~
	~~:<math>\int_{0}^{\infty}f\left(x\right)dx=\int_{0}^{\infty}f\left(x\right)e^{x}e^{~~-~~x}dx=\int_{0}^{\infty}g\left(x\right)e^{-x}dx</math>~~
	~~where <math>g\left(x\right) := e^{x} f\left(x\right)</math>. For~~ the ~~last integral~~
	~~one then uses Gauss-Laguerre quadrature. Note,~~ that ~~while this approach~~ works
	from ~~an analytical perspective~~, ~~it is not always numerically stable~~.

	~~==Generalized Gauss–Laguerre quadrature==~~

	~~More generally, one~~ can also ~~consider integrands~~ that ~~have a known <math>x^\alpha</math> power-law singularity at ''x''=0, for some real~~ number <~~math>\alpha~~ > -1<~~/math~~>~~, leading~~ to ~~integrals of the form:~~
	~~:<math>\int_{0}^{+\infty} x^\alpha e^{~~-~~x} f(x)\,dx~~.~~</math>~~
	~~This allows~~ one to ~~efficiently evaluate such integrals~~ for ~~polynomial or smooth ''f''(''x'') even when α is not an integer~~.~~<ref>{{cite journal\|first1=Philip \|last1=Rabinowitz \|authorlink1= Philip Rabinowitz (mathematician) \|first2=George \|last2=Weiss \| title=Tables~~ of ~~Abscissas~~ and ~~Weights for Numerical Evaluation~~ of ~~Integrals of the form <math>\int_0^{\infty} \exp(-x) x^n f(x) dx<~~/~~math> \| journal=Mathematical Tables and Other Aids to Computation \|volume=13 \| pages=285–294 \| year=1959 \| doi=10~~.~~1090~~/~~S0025-5718-1959-0107992-3 }}</ref>~~

	~~==References==~~
	~~<references/>~~
	*{{cite journal \| first1=Herbert E. ~~\|last1=Salzer~~
	~~\|first2=Ruth \|last2=Zucker~~
	~~\|title=Table of zeros~~ and ~~weight factors of~~ the ~~first fifteen Laguerre polynomials~~
	~~\|journal=Bull~~. Am. ~~Math. Soc.~~
	~~\|year=1949 \| volume=55~~
	~~\|pages=1004–1012 \| doi=~~
	~~10.1090/S0002~~-~~9904-1949-09327-8 }}~~
	*{{cite journal\|first1=P. \|last1=Concus \| first2=D. \|last2=Cassatt
	~~\|first3=G. \|last3=Jaehnig \| first4=E. \| last4=Melby~~
	~~\|title=Tables~~ for the ~~evaluation~~ of ~~int_0^infinity x^beta exp(-x) f(x) dx by Gauss-Laguerre quadrature~~
	~~\|journal=Math~~. ~~Comp~~.
	~~\|volume=17~~
	~~\|pages=245–256 \|year=1963 \| doi=10.1090/S0025~~-~~5718~~-~~1963-0158534-9 }}~~
	*{{cite journal
	~~\|first1=T~~. S. ~~\| last1=Shao \| first2=T~~. ~~C. \| last2=Chen~~
	~~\|first3=R. M. \| last3=Frank~~
	~~\|title=Table of zeros~~ and ~~Gaussian Weights of certain Associated Laguerre Polynomials~~ and ~~the related Hermite Polynomials~~
	~~\|year=1964~~
	~~\|jstor=2002946~~
	~~\|journal=Math. Comput.~~
	~~\|volume=18 \|issue=88 \| pages=598–616 \| mr=0166397 \|doi=10~~.~~1090/S0025-5718-1964-0166397-1 }}~~
	*{{cite journal
	~~\|first1=Sven \| last1=Ehrich~~
	~~\|title=On stratified extensions~~ of ~~Gauss~~-~~Laguerre~~ and ~~Gauss~~-~~Hermite quadrature formulas~~
	~~\|year=2002 \| journal=J~~. ~~Comput. Appl. Math. \| volume=140 \| issue=1~~-2
	~~\|pages=291–299 \| doi=~~
	~~10.1016/S0377~~-~~0427(01)00407-1~~
	}}
	*{{ cite web
	~~\|first1= R~~. ~~J. \| last1 = Mathar~~
	~~\|url=http~~:~~//vixra~~.~~org/abs/1303.0013~~
	~~\|title=Gauss-Laguerre and Gauss-Hermite Quadrature on 64~~, ~~96 and 128 Nodes~~
	~~\|year=2013~~
	}}

	~~==External links==~~
	* [http://www.mathworks.~~com/matlabcentral/fileexchange/8067-gauss-laguerre Matlab routine for Gauss–Laguerre quadrature]~~
	* [http://people.sc.fsu.edu/~jburkardt/m_src/gen_laguerre_rule/gen_laguerre_rule.html generalized Gauss–Laguerre quadrature], [[free software]] in Matlab, C++, and Fortran.

	~~{{DEFAULTSORT:Gauss-Laguerre quadrature}}~~
	~~[[Category:Numerical integration (quadrature)]]~~

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← Older revision		Revision as of 08:54, 19 March 2013
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	~~So your company has a video project that they~~'~~d like to see produced. Maybe it~~'~~s web video content, possibly it~~'s an ~~internal video~~ for ~~sales training~~, ~~or you wish to capture an upcoming corporate event~~.<br><br><br><br>Use social websites and bookmarking sites to market your videos. MySpace and Facebook as well as Reddit, Digg, StumbleUpon and a few other sites can help you promote your video and also you always experience the ~~chance~~ of ~~the usb ports going viral.~~<br><br>~~The content you created has end up being distributed straightforward so that will try this. One method of doing this would be to create quality content, record it with camtasia yet another software~~ and ~~post it on youtube. Nowadays a lot of people use p2p. This could potentially be a goldmine if you tap straight into it.~~<br><br>~~Although the internet on the Dash~~ is ~~great and quick~~, ~~the design may acquire a bit horrible~~. ~~There is no web address bar present very first~~. ~~In order to be able to type within a web address~~, ~~you might need to click on menu on~~-~~line application then click regarding link to go to web address~~. ~~To make it easier, you might need to add simple~~ . ~~websites in your own favorites so you should access them easily out from the main screen or by means of favorites tab on the internet's menu~~.~~<br><br>The second requirement for creating really own website is hosting~~. [http://www.~~quora~~.com/~~What~~-is-~~financial~~-~~spread-betting what is financial spread betting]'s~~ that~~? Think about~~ it ~~considering that house you build during your land~~. ~~Ought to you don't possess a house of your titled land~~, ~~you~~ can'~~t live for it. That~~'~~s operates~~ for ~~a website~~, ~~products and solutions do never hosting, you would not see any~~ of ~~your posts~~, ~~pics and vids when you press on Enter after typing with your website deal with~~. ~~For example if Google.com doesn~~'~~t have hosting,~~ when ~~you click on the Enter key, you cant see anything, well maybe a notice out of your domain registrar informing the blog~~ is not ~~up thus far~~.<br><br>~~"I Wanna Be a Cowboy"~~- ~~Boys Don't Cry~~ (~~1986~~)~~. I cringe~~ to ~~confess that One time i owned this song on 45~~. ~~But after re~~-~~listening to it two decades later, I wish I may possibly a order value.~~<br><br>~~Don't think as a parent that carbohydrates relax~~ of ~~this type though~~. ~~Bollywood actors~~ and ~~actresses are masters~~ of ~~flirtation~~ and ~~employ~~ of ~~other body parts~~ and ~~props to portray sexuality, which sometimes results more tantalizing result than a simple kiss would~~. ~~Take note of your children's level of development, as well how much exposure to sensuality is healthy their own behalf~~.~~<br><br>When do you plan to promote your stuff~~. ~~Well internet marketing is unlike if you are in a brick~~ and ~~mortar store that has certain hours of operation~~. ~~All though if you are socially communicate with~~ people ~~you need online usually they are~~. ~~As an example lets take twitter~~, ~~there are particular hours at the time that positioned on prospected customers are on~~.		In [[numerical analysis]] '''Gauss–Laguerre quadrature''' is an extension of [[Gaussian quadrature]] method for approximating the value of integrals of the following kind:

			:<math>\int_{0}^{+\infty} e^{-x} f(x)\,dx.</math>

			In this case

			:<math>\int_{0}^{+\infty} e^{-x} f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i)</math>

			where ''x''<sub>''i''</sub> is the ''i''-th root of [[Laguerre polynomial]] ''L''<sub>''n''</sub>(''x'') and the weight ''w''<sub>''i''</sub> is given by
			<ref name="AS">[[Milton Abramowitz\|Abramowitz, M.]] & [[Irene Stegun\|Stegun, I. A.]], ''Handbook of Mathematical Functions'', 10th printing with corrections (1972), Dover, ISBN 978-0-486-61272-0. Equation 25.4.45.[http://www.nrbook.com/abramowitz_and_stegun/page_890.htm access online]</ref>

			:<math>w_i = \frac {x_i} {(n+1)^2[L_{n+1}(x_i)]^2}.</math>

			==For more general functions==

			To integrate the function <math>f</math> we apply the following transformation
			:<math>\int_{0}^{\infty}f\left(x\right)dx=\int_{0}^{\infty}f\left(x\right)e^{x}e^{-x}dx=\int_{0}^{\infty}g\left(x\right)e^{-x}dx</math>
			where <math>g\left(x\right) := e^{x} f\left(x\right)</math>. For the last integral
			one then uses Gauss-Laguerre quadrature. Note, that while this approach works
			from an analytical perspective, it is not always numerically stable.

			==Generalized Gauss–Laguerre quadrature==

			More generally, one can also consider integrands that have a known <math>x^\alpha</math> power-law singularity at ''x''=0, for some real number <math>\alpha > -1</math>, leading to integrals of the form:
			:<math>\int_{0}^{+\infty} x^\alpha e^{-x} f(x)\,dx.</math>
			This allows one to efficiently evaluate such integrals for polynomial or smooth ''f''(''x'') even when α is not an integer.<ref>{{cite journal\|first1=Philip \|last1=Rabinowitz \|authorlink1= Philip Rabinowitz (mathematician) \|first2=George \|last2=Weiss \| title=Tables of Abscissas and Weights for Numerical Evaluation of Integrals of the form <math>\int_0^{\infty} \exp(-x) x^n f(x) dx</math> \| journal=Mathematical Tables and Other Aids to Computation \|volume=13 \| pages=285–294 \| year=1959 \| doi=10.1090/S0025-5718-1959-0107992-3 }}</ref>

			==References==
			<references/>
			*{{cite journal \| first1=Herbert E. \|last1=Salzer
			\|first2=Ruth \|last2=Zucker
			\|title=Table of zeros and weight factors of the first fifteen Laguerre polynomials
			\|journal=Bull. Am. Math. Soc.
			\|year=1949 \| volume=55
			\|pages=1004–1012 \| doi=
			10.1090/S0002-9904-1949-09327-8 }}
			*{{cite journal\|first1=P. \|last1=Concus \| first2=D. \|last2=Cassatt
			\|first3=G. \|last3=Jaehnig \| first4=E. \| last4=Melby
			\|title=Tables for the evaluation of int_0^infinity x^beta exp(-x) f(x) dx by Gauss-Laguerre quadrature
			\|journal=Math. Comp.
			\|volume=17
			\|pages=245–256 \|year=1963 \| doi=10.1090/S0025-5718-1963-0158534-9 }}
			*{{cite journal
			\|first1=T. S. \| last1=Shao \| first2=T. C. \| last2=Chen
			\|first3=R. M. \| last3=Frank
			\|title=Table of zeros and Gaussian Weights of certain Associated Laguerre Polynomials and the related Hermite Polynomials
			\|year=1964
			\|jstor=2002946
			\|journal=Math. Comput.
			\|volume=18 \|issue=88 \| pages=598–616 \| mr=0166397 \|doi=10.1090/S0025-5718-1964-0166397-1 }}
			*{{cite journal
			\|first1=Sven \| last1=Ehrich
			\|title=On stratified extensions of Gauss-Laguerre and Gauss-Hermite quadrature formulas
			\|year=2002 \| journal=J. Comput. Appl. Math. \| volume=140 \| issue=1-2
			\|pages=291–299 \| doi=
			10.1016/S0377-0427(01)00407-1
			}}
			*{{ cite web
			\|first1= R. J. \| last1 = Mathar
			\|url=http://vixra.org/abs/1303.0013
			\|title=Gauss-Laguerre and Gauss-Hermite Quadrature on 64, 96 and 128 Nodes
			\|year=2013
			}}

			==External links==
			* [http://www.mathworks.com/matlabcentral/fileexchange/8067-gauss-laguerre Matlab routine for Gauss–Laguerre quadrature]
			* [http://people.sc.fsu.edu/~jburkardt/m_src/gen_laguerre_rule/gen_laguerre_rule.html generalized Gauss–Laguerre quadrature], [[free software]] in Matlab, C++, and Fortran.

			{{DEFAULTSORT:Gauss-Laguerre quadrature}}
			[[Category:Numerical integration (quadrature)]]

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