en>Rjwilmsi: /* References */Journal cites, Added 1 doi to a journal cite using AWB (10365)

2014-08-13T13:02:27Z

References: Journal cites, Added 1 doi to a journal cite using AWB (10365)

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	~~{{DISPLAYTITLE: Quantum ''q''-Krawtchouk polynomials}}~~
	In mathematics, the '''quantum ''q''-Krawtchouk polynomials''' are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]]. {{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.

	~~==Definition==~~

	The ~~polynomials~~ are ~~given~~ in ~~terms~~ of [[~~basic hypergeometric function]~~]s and the ~~[[Pochhammer symbol]] by~~		I experienced my first implant when We were very young already. The thrill I was ready 8 years of. I had an accident with my bicycle and lost a one's teeth. An implant is still the best practice to replace a tooth nevertheless it's also pretty expensive.<br><br>Learn within tips to saving money on your next big EVENT! Many people a Wedding or Special Occassion.... This Even Planning Expert features the ANSWERS!<br><br>You also want to from their cubicles. Their office should make you are feeling warm and welcome. However, many don't offer this. This is important because should don't feel warm and welcomed, that is as bad when you travel to sit in the chair as well as having a dentist work to your teeth. When aren't sure as to what their offices look like and are generally already globe San Diego area, then ask think about a tour.<br><br>Crest Weekly Clean Intensive Cleaning Paste retails for $4.79. The tube contains enough product for sixteen uses. Entry of [http://www.Answers.com/topic/lessons+claims lessons claims] that this product contains an ingredient that is in dental in tampa fl - [https://www.youtube.com/watch?v=4To0cBm6IsM browse around these guys], order to what dentist use inside office domestic cleaning. The package has the familiar red and blue colors associated without the pain . Crest brand name and is located in the toothpaste aisle. Crest is a familiar name in tooth care which is known for it's quality products and affordable asking prices. I certainly want to do what I can to rid my teeth of the data that I am a daily coffee drinker and also the low price definitely spoke to to me. I was quite excited to try this product.<br><br>Regular checkups can help identify indication of dentist oral cancer before it's too late. Gum disease is one of several main purpose of tooth lowering. If you loved this article and you would like to obtain more info concerning dental in tampa fl - [https://www.youtube.com/watch?v=4To0cBm6IsM browse around these guys], please visit our own page. Periodic visits to the doctor will be beneficial in spotting it's signs in era. Take an estimate of your treatment required so a person simply can plan how really can pay for doing it.<br><br>Again, it really is further. Dental problems don't stop as mouth. When plaque and tartar have formed for the teeth, the gums are inflamed, and infection initiated a policy of to spread, every time a dog or cat bites down to chew, that infection will then be spread in the blood pool. The blood flows all through body, carrying this infection to vital organs.<br><br>The big question for many people patients is, "How much will this cost?" For that fast, free quote through your Los Angeles Dental Implant professional, call Dr. Arthur Kezian at (323) 467-2777 during regular business periods. You'll be glad you did!
	:<~~math~~>~~\displaystyle~~ <~~/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=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>Headbomb: Various citation cleanup (identifiers mostly) using AWB

2011-09-05T07:02:47Z

Various citation cleanup (identifiers mostly) using AWB

New page

{{DISPLAYTITLE: Quantum ''q''-Krawtchouk polynomials}}
In mathematics, the '''quantum ''q''-Krawtchouk polynomials''' are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]]. {{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.

==Definition==

The polynomials are given in terms of [[basic hypergeometric function]]s and the [[Pochhammer symbol]] by
:<math>\displaystyle </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=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]]

Continuous q-Jacobi polynomials - Revision history

en>Rjwilmsi: /* References */Journal cites, Added 1 doi to a journal cite using AWB (10365)

en>Headbomb: Various citation cleanup (identifiers mostly) using AWB