Klinkenberg correction - Revision history

94.211.206.24 at 09:07, 8 May 2014

2014-05-08T09:07:47Z

← Older revision		Revision as of 11:07, 8 May 2014
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	~~In mathematics, the '''''q''-Racah polynomials''' are~~ a ~~family~~ of ~~basic hypergeometric~~ [~~[orthogonal polynomials]] in the basic [[Askey scheme]], introduced by {{harvtxt\|Askey\|Wilson\|1979}}~~. ~~{{harvs\|txt \| last1~~=~~Koekoek \| first1~~=~~Roelof \| last2~~=~~Lesky \| first2~~=~~Peter A~~. ~~\| last3=Swarttouw \| first3=René F~~. ~~\| title=Hypergeometric orthogonal polynomials~~ and ~~their q~~-~~analogues \| publisher=[[Springer~~-~~Verlag]] \| location=Berlin, New York \| series=Springer Monographs in Mathematics \| isbn=978~~-3-~~642~~-~~05013~~-~~8 \| doi=10.1007/978~~-3-~~642~~-~~05014~~-~~5 \| mr=2656096 \| year=2010\|loc=14}} give~~ a ~~detailed list of their properties~~.		\ոEven though salads possess a properly-ԁeserved reputation for being Һeɑlthfսl, lots of pеople minimize or remove the health advantages by ѕlathering thеir salad [http://paytube.tv/yamaze/groups/does-vigrx-plus-really-works-eat-correctly-and-experience-the-very-best-you-may-have-at-any-time-noticed/ vigrx plus in johannesburg] abundant dressings. 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	=~~=Definition==~~

	The ~~polynomials are given in terms of [[basic hypergeometric function~~]]s and ~~the [[Pochhammer symbol]] by~~
	:<~~math~~>~~p_n(q^{-x}+q^{x+~~1~~}cd;a~~,b,c,~~d;q) = {}_4\phi_3\left[\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\\~~
	~~aq&bdq&cq\\ \end{matrix};q;q\right]~~<~~/math~~>
	~~They are sometimes given with changes~~ of ~~variables~~ as
	:<~~math~~>~~W_n(x;~~a,b,c,~~N;q) = {}_4\phi_3\left[\begin{matrix} q^{~~-~~n} &abq^{n+1}&q^{-x}&cq^{x-n}\\~~
	~~aq&bcq&q^{-N}\\ \end{matrix};q;q\right]~~<~~/math~~>

	~~==Orthogonality==~~
	~~{{Empty section\|date=September 2011}}~~

	~~==Recurrence~~ and ~~difference relations==~~
	~~{{Empty section\|date=September 2011}}~~

	~~==Rodrigues formula==~~
	~~{{Empty section\|date=September 2011}}~~

	~~==Generating function==~~
	~~{{Empty section\|date=September 2011}}~~

	~~==Relation~~ to other ~~polynomials==~~
	~~{{Empty section\|date=September 2011}}~~

	~~==References==~~

	*{{Citation \| last1=Askey \| first1=Richard \| last2=Wilson \| first2=James \| title=A ~~set~~ of ~~orthogonal polynomials that generalize~~ the ~~Racah coefficients~~ or ~~6-j symbols \| doi=10~~.~~1137/0510092 \| mr=541097 \| year=1979 \| journal=SIAM Journal on Mathematical Analysis \| issn=0036-1410 \| volume=10 \| issue=5 \| pages=1008–1016}}~~
	*{{Citation \| last1=Gasper \| first1=George \| last2=Rahman \| first2=Mizan \| title=Basic hypergeometric series \| publisher=[[Cambridge University Press]] \| edition=2nd \| series=Encyclopedia of Mathematics and ~~its Applications \| isbn=978-0-521-83357-8 \| doi=10~~.~~2277/0521833574 \| mr=2128719 \| year=2004 \| volume=96}}~~
	*{{Citation \| last1=Koekoek \| first1=Roelof \| last2=Lesky \| first2=Peter A. ~~\| last3=Swarttouw \| first3=René F~~. ~~\| title=Hypergeometric orthogonal polynomials~~ and ~~their q-analogues \| publisher=[[Springer-Verlag]] \| location=Berlin~~, ~~New York \| series=Springer Monographs~~ in ~~Mathematics \| isbn=978-3-642-05013-8 \| doi=10~~.~~1007/978-3-642-05014-5 \| mr=2656096 \| year=2010}}~~
	*{{dlmf\|id=18\|title=\|first=Tom H. ~~\|last=Koornwinder\|first2=Roderick S~~. ~~C.\|last2= Wong\|first3=Roelof \|last3=Koekoek\|\|first4=René F~~. ~~\|last4=Swarttouw}}~~

	~~[[Category:Orthogonal polynomials]]~~
	~~[[Category:Q-analogs]]~~
	~~[[Category:Special hypergeometric functions]]~~

153.90.118.189 at 22:44, 29 August 2013

2013-08-29T22:44:06Z

← Older revision		Revision as of 00:44, 30 August 2013
Line 1:		Line 1:
	~~They~~'~~re always ready to help~~, ~~and they~~'~~re always making changes to the site to make sure you won~~'~~t have troubles in the first place. Medical word press themes give you the latest medical designs. I thought about what would happen by placing~~ a ~~text widget~~ in the ~~sidebar beneath my banner ad~~, ~~and so it went~~. ~~If you are using videos on your site then this is the plugin to use~~. ~~After activating~~, ~~you will find their website link and get the activation code from~~ their ~~website~~. ~~<br><br>~~		{{DISPLAYTITLE: ''q''-Racah polynomials}}
			In mathematics, the '''''q''-Racah polynomials''' are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], introduced by {{harvtxt\|Askey\|Wilson\|1979}}. {{harvs\|txt \| last1=Koekoek \| first1=Roelof \| last2=Lesky \| first2=Peter A. \| last3=Swarttouw \| first3=René F. \| title=Hypergeometric orthogonal polynomials and their q-analogues \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Springer Monographs in Mathematics \| isbn=978-3-642-05013-8 \| doi=10.1007/978-3-642-05014-5 \| mr=2656096 \| year=2010\|loc=14}} give a detailed list of their properties.

	~~Generally, for my private income-making market websites, I will thoroughly research~~ and ~~discover~~ the leading 10 most worthwhile niches to venture into. Wordpress have every reason with it which promote wordpress development. Our Daily Deal Software plugin brings the simplicity of setting up a Word - Press blog to the daily deal space. t need to use the back button or the URL to get to your home page. Aided by ~~the completely foolproof j~~ - ~~Query color selector~~, ~~you're able to change the colors of factors of your theme a the click on the screen~~, with ~~very little previous web site design experience.~~ <br><br>~~It is very easy~~ to ~~install Word~~ - ~~Press blog or website~~. ~~Word~~ - Press ~~has ensured the users~~ of ~~this open source blogging platform do not have to troubleshoot on their own, or seek outside help~~. ~~Should you have any questions relating to wherever as well as how you can make use of [http:~~/~~/xyz~~.~~ms/wordpress_backup_plugin_731523 backup plugin], you possibly can e mail us on the site~~. ~~You can now search through the thousands of available plugins to add all kinds of functionality to your Word~~ - ~~Press site. User friendly features and flexibility that Word~~ - ~~Press has to offer is second to none. So~~, ~~if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you~~ in ~~each and every best possible way. <br><br>Word~~ - ~~Press installation is very easy and hassle free~~. But the Joomla was created as the CMS over years of hard work. To do this, you should link your posts to other relevant posts that you've created. 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. The popularity of Word - ~~Press has increased the demand for Word~~ - ~~Press themes and these themes sells like hot cake on the internet. <br><br>You will know which of your Word~~ - ~~Press blog posts are attracting more unique visitors which in turn will help you develop better products and services for your customers. Here's a list of some exciting Word~~ - ~~Press features that have created waves in the web development industry:~~. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. ~~Web developers and newbies alike will have the ability to extend your web site and fit other incredible functions with out having to spend more~~. ~~Press CTRL and the numbers one to six to choose your option~~.		==Definition==

			The polynomials are given in terms of [[basic hypergeometric function]]s and the [[Pochhammer symbol]] by
			:<math>p_n(q^{-x}+q^{x+1}cd;a,b,c,d;q) = {}_4\phi_3\left[\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\\
			aq&bdq&cq\\ \end{matrix};q;q\right]</math>
			They are sometimes given with changes of variables as
			:<math>W_n(x;a,b,c,N;q) = {}_4\phi_3\left[\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&cq^{x-n}\\
			aq&bcq&q^{-N}\\ \end{matrix};q;q\right]</math>

			==Orthogonality==
			{{Empty section\|date=September 2011}}

			==Recurrence and difference relations==
			{{Empty section\|date=September 2011}}

			==Rodrigues formula==
			{{Empty section\|date=September 2011}}

			==Generating function==
			{{Empty section\|date=September 2011}}

			==Relation to other polynomials==
			{{Empty section\|date=September 2011}}

			==References==

			*{{Citation \| last1=Askey \| first1=Richard \| last2=Wilson \| first2=James \| title=A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols \| doi=10.1137/0510092 \| mr=541097 \| year=1979 \| journal=SIAM Journal on Mathematical Analysis \| issn=0036-1410 \| volume=10 \| issue=5 \| pages=1008–1016}}
			*{{Citation \| last1=Gasper \| first1=George \| last2=Rahman \| first2=Mizan \| title=Basic hypergeometric series \| publisher=[[Cambridge University Press]] \| edition=2nd \| series=Encyclopedia of Mathematics and its Applications \| isbn=978-0-521-83357-8 \| doi=10.2277/0521833574 \| mr=2128719 \| year=2004 \| volume=96}}
			*{{Citation \| last1=Koekoek \| first1=Roelof \| last2=Lesky \| first2=Peter A. \| last3=Swarttouw \| first3=René F. \| title=Hypergeometric orthogonal polynomials and their q-analogues \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Springer Monographs in Mathematics \| isbn=978-3-642-05013-8 \| doi=10.1007/978-3-642-05014-5 \| mr=2656096 \| year=2010}}
			*{{dlmf\|id=18\|title=\|first=Tom H. \|last=Koornwinder\|first2=Roderick S. C.\|last2= Wong\|first3=Roelof \|last3=Koekoek\|\|first4=René F. \|last4=Swarttouw}}

			[[Category:Orthogonal polynomials]]
			[[Category:Q-analogs]]
			[[Category:Special hypergeometric functions]]

en>R'n'B: Fix links to disambiguation page Permeability

2011-04-19T13:24:22Z

Fix links to disambiguation page Permeability

New page

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Generally, for my private income-making market websites, I will thoroughly research and discover the leading 10 most worthwhile niches to venture into. Wordpress have every reason with it which promote wordpress development. Our Daily Deal Software plugin brings the simplicity of setting up a Word - Press blog to the daily deal space. t need to use the back button or the URL to get to your home page. Aided by the completely foolproof j - Query color selector, you're able to change the colors of factors of your theme a the click on the screen, with very little previous web site design experience. It is very easy to install Word - Press blog or website. Word - Press has ensured the users of this open source blogging platform do not have to troubleshoot on their own, or seek outside help. Should you have any questions relating to wherever as well as how you can make use of [http://xyz.ms/wordpress_backup_plugin_731523 backup plugin], you possibly can e mail us on the site. You can now search through the thousands of available plugins to add all kinds of functionality to your Word - Press site. User friendly features and flexibility that Word - Press has to offer is second to none. So, if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you in each and every best possible way. Word - Press installation is very easy and hassle free. But the Joomla was created as the CMS over years of hard work. To do this, you should link your posts to other relevant posts that you've created. 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. The popularity of Word - Press has increased the demand for Word - Press themes and these themes sells like hot cake on the internet. You will know which of your Word - Press blog posts are attracting more unique visitors which in turn will help you develop better products and services for your customers. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. Web developers and newbies alike will have the ability to extend your web site and fit other incredible functions with out having to spend more. Press CTRL and the numbers one to six to choose your option.