en>BD2412: /* Definition */Fixing links to disambiguation pages, replaced: AWB

2014-06-18T16:59:00Z

Definition: Fixing links to disambiguation pages, replaced: → [[Quotient space (topology)| using [[Project:AWB|AWB

← Older revision		Revision as of 18:59, 18 June 2014
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	~~{{distinguish\|Rogers–Szegő polynomials}}~~		Trying to figure out which desktop laptop to get can be really difficult. You might not know about all the current specs and other characteristics that are offered correct now. If you need some support, this post is going to provide you with some needed data in order to guide you by means of the method.<br><br>Use virus protection application. With no such a program, malicious computer software may infect your system. Malicious software program applications can hijack your individual info and slow down your laptop processing speed. There are really a handful of applications that will automatically scan and fix your desktop.<br><br>Building your personal laptop can save a lot of income, although at the very same time making a technique that is twice as effective as you would get if you purchased it from a manufacturer. Building your own personal computer saves time, cash, and cuts out the middle man. If you are concerned with reading, you will possibly wish to study about [http://www.evs-ems.com/ china electronics manufacturing]. Start off creating your personal today!<br><br>If you want to save income when getting a desktop pc, take into account getting a refurbished model. You can appear at the sites of main laptop producers such as HP or Dell, exactly where you will find fantastic deals on computers that have been returned to the organization, fixed and sold at a discount price.<br><br>Do not overlook the high quality of the desktop computer monitor when taking into consideration your obtain. The specs of the actual pc may be amazing, but if the monitor is poor, your all round encounter will be negative also. To discover more, consider looking at: [http://www.electronic-design-manufacture.com/ pcb assemblies]. Remember, it really is the monitor that you"ll have the most interaction with, so be prepared to commit more to get one particular you like.<br><br>For the greatest deal when buying a new desktop pc, shop during and right after back to school time or just just before Christmas. These are the times when computer companies offer you great offers on a lot of of their very best promoting computer systems. Pc companies will also offer you bundles of desktops and printers that can save you additional income.<br><br>Attempt to customize your purchase when ordering your pc. If you are ordering straight from the manufacturer, you need to be capable to upgrade individual elements. For instance, you should be in a position to get much more storage space for a greater charge. You may well be able to get a diverse video card by paying a bit much more. Appear into various companies to make confident you have this alternative.<br><br>One advantage of purchasing a desktop rather than a laptop pc is the wider range of choices. If you buy a laptop, you are limited to the screen, keyboard and trackpad that is built into the machine. If you buy a desktop, choose the program and peripherals you require most.<br><br>Do not get sucked into waiting as well lengthy for price tag drops. [http://www.evs-ems.com/ Electronics Manufacturers In China] contains additional resources about the meaning behind this enterprise. Some people only spend attention to what bargains are the greatest. Even so, they don"t do something, as they feel they can get a great deal soon. The very best bargains have a tiny margin amongst them. After you discover an attractive deal, take it!<br><br>How do you really feel about your understanding about individual desktop computers now? Use what you"ve learned to help you make a intelligent buying selection. There are several brands and distinct kinds of desktop computers, so now that you know much more about them you can determine which one performs for you..<br><br>Should you liked this article in addition to you would want to get more information about [http://independent.academia.edu/JessieBirda/Posts need health insurance] kindly check out the web page.
	~~In mathematics,~~ the ~~'''Rogers polynomials''', also called '''Rogers–Askey–Ismail polynomials'''~~ and ~~'''continuous q-ultraspherical polynomials'''~~, ~~are a family of [[orthogonal polynomials]] introduced~~ by ~~{{harvs\|txt\|authorlink=Leonard James Rogers\|last=Rogers\|year1=1892\|year2=1893\|year3=1894}} in the course~~ of ~~his work on~~ the ~~[[Rogers–Ramanujan identities]]~~. ~~They are ''q''-analogs of [[ultraspherical polynomials]], and are the [[Macdonald polynomials]] for the special case of the ''A''~~<~~sub~~>1<~~/sub~~> ~~[[affine root~~ system~~]] {{harv\|Macdonald\|2003\|loc=p~~.~~156}}.~~

	~~{{harvtxt\|Askey\|Ismail\|1983}}~~ and ~~{{harvtxt\|Gasper\|Rahman\|2004\|loc=7~~.~~4}} discuss the properties~~ of ~~Rogers polynomials in detail~~.

	~~==Definition==~~

	~~The Rogers polynomials~~ can ~~be defined in terms~~ of the ~~descending Pochhammer symbol~~ and the [~~[basic hypergeometric series~~]~~] by~~
	:<~~math~~> ~~C_n(x;\beta\|q) = \frac{(\beta;q)_n}{(q;q)_n}e^{in\theta} {}_2\phi_1(q^{-n}~~,~~\beta;\beta^{-1}q^{1-n};q~~,~~q\beta^{-1}e^{-2i\theta})~~<~~/math~~>
	~~where ''x'' = cos(''θ'')~~.

	~~==References==~~

	*{{Citation \| last1=Askey \| first1=Richard \| last2=Ismail \| first2=Mourad E. H. \| editor1-last=Erdős \| editor1-first=Paul \| title=Studies in pure mathematics. To ~~the memory of Paul Turán. \| url=~~http://~~books~~.~~google~~.com/~~books?id=WePuAAAAMAAJ \| publisher=Birkhäuser \| location=Basel~~, ~~Boston~~, ~~Berlin \| isbn=978-3-7643-1288-6 978-3-7643-1288-6 \| mr=820210 \| year=1983 \| chapter=A generalization~~ of ~~ultraspherical polynomials \| pages=55–78}}~~
	*{{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=Macdonald \| first1=I. G. ~~\| author1-link=Ian G. Macdonald \| title=Affine Hecke algebras and orthogonal polynomials \| publisher=[[Cambridge University Press]] \| series=Cambridge Tracts~~ in ~~Mathematics \| isbn=978-0-521-82472-9 \| doi=10~~.~~1017/CBO9780511542824 \| mr=1976581 \| year=2003 \| volume=157}}~~
	*{{Citation \| last1=Rogers \| first1=L. J. ~~\| title=On~~ the ~~expansion~~ of ~~some infinite products \| doi=10~~.~~1112/plms/s1-24~~.1.~~337 \| jfm=25~~.~~0432.01 \| year=1892 \| journal=Proc. London Math. Soc. \| volume=24 \| issue=1 \| pages=337–352 }}~~
	*{{Citation \| last1=Rogers \| first1=L. J. \| title=Second Memoir on the Expansion of certain Infinite Products \| doi=10.1112/~~plms~~/s1-25.1.~~318 \| year=1893 \| journal=Proc~~. ~~London Math~~. ~~Soc~~. ~~\| volume=25 \| issue=1 \| pages=318–343}}~~
	*{{Citation \| last1=Rogers \| first1=L. J. ~~\| title=Third Memoir on the Expansion of certain Infinite Products \| doi=10~~.~~1112~~/~~plms~~/~~s1-26~~.1.~~15 \| year=1894 \| journal=Proc~~. ~~London Math. Soc. \| volume=26 \| issue=1 \| pages=15–32}}~~

	~~[[Category:Orthogonal polynomials]]~~
	~~[[Category:Q-analogs]]~~

en>Sullivan.t.j: /* Properties / Completion with respect to the Alexiewicz norm*.

2011-11-10T20:31:24Z

Properties: Completion *with respect to the Alexiewicz norm*.

New page

{{distinguish|Rogers–Szegő polynomials}}
In mathematics, the '''Rogers polynomials''', also called '''Rogers–Askey–Ismail polynomials''' and '''continuous q-ultraspherical polynomials''', are a family of [[orthogonal polynomials]] introduced by {{harvs|txt|authorlink=Leonard James Rogers|last=Rogers|year1=1892|year2=1893|year3=1894}} in the course of his work on the [[Rogers–Ramanujan identities]]. They are ''q''-analogs of [[ultraspherical polynomials]], and are the [[Macdonald polynomials]] for the special case of the ''A''<sub>1</sub> [[affine root system]] {{harv|Macdonald|2003|loc=p.156}}.

{{harvtxt|Askey|Ismail|1983}} and {{harvtxt|Gasper|Rahman|2004|loc=7.4}} discuss the properties of Rogers polynomials in detail.

==Definition==

The Rogers polynomials can be defined in terms of the descending Pochhammer symbol and the [[basic hypergeometric series]] by
:<math> C_n(x;\beta|q) = \frac{(\beta;q)_n}{(q;q)_n}e^{in\theta} {}_2\phi_1(q^{-n},\beta;\beta^{-1}q^{1-n};q,q\beta^{-1}e^{-2i\theta})</math>
where ''x'' = cos(''θ'').

==References==

*{{Citation | last1=Askey | first1=Richard | last2=Ismail | first2=Mourad E. H. | editor1-last=Erdős | editor1-first=Paul | title=Studies in pure mathematics. To the memory of Paul Turán. | url=http://books.google.com/books?id=WePuAAAAMAAJ | publisher=Birkhäuser | location=Basel, Boston, Berlin | isbn=978-3-7643-1288-6 978-3-7643-1288-6 | mr=820210 | year=1983 | chapter=A generalization of ultraspherical polynomials | pages=55–78}}
*{{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=Macdonald | first1=I. G. | author1-link=Ian G. Macdonald | title=Affine Hecke algebras and orthogonal polynomials | publisher=[[Cambridge University Press]] | series=Cambridge Tracts in Mathematics | isbn=978-0-521-82472-9 | doi=10.1017/CBO9780511542824 | mr=1976581 | year=2003 | volume=157}}
*{{Citation | last1=Rogers | first1=L. J. | title=On the expansion of some infinite products | doi=10.1112/plms/s1-24.1.337 | jfm=25.0432.01 | year=1892 | journal=Proc. London Math. Soc. | volume=24 | issue=1 | pages=337–352 }}
*{{Citation | last1=Rogers | first1=L. J. | title=Second Memoir on the Expansion of certain Infinite Products | doi=10.1112/plms/s1-25.1.318 | year=1893 | journal=Proc. London Math. Soc. | volume=25 | issue=1 | pages=318–343}}
*{{Citation | last1=Rogers | first1=L. J. | title=Third Memoir on the Expansion of certain Infinite Products | doi=10.1112/plms/s1-26.1.15 | year=1894 | journal=Proc. London Math. Soc. | volume=26 | issue=1 | pages=15–32}}

[[Category:Orthogonal polynomials]]
[[Category:Q-analogs]]

Alexiewicz norm - Revision history

en>BD2412: /* Definition */Fixing links to disambiguation pages, replaced: AWB

en>Sullivan.t.j: /* Properties */ Completion *with respect to the Alexiewicz norm*.

en>Sullivan.t.j: /* Properties / Completion with respect to the Alexiewicz norm*.