en>Hakamiso: the names cannot be easily linked that way, and it makes the article confusing.

2013-07-06T20:20:56Z

the names cannot be easily linked that way, and it makes the article confusing.

← Older revision		Revision as of 22:20, 6 July 2013
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	~~Medical Light Therapist Leigh Corredor from La Ronge, enjoys to spend time bonsai trees~~, ~~ganhando dinheiro na internet and crafts. During~~ the ~~recent month or~~ two ~~has visited to spots for example Monastery~~ of the ~~Hieronymites~~ and ~~Tower~~ of ~~Belém~~ in ~~Lisbon.~~<br><br>~~Here is my web page~~: [http://~~comoconseguirdinheiro~~.~~comoganhardinheiro101~~.~~com ganhar dinheiro~~]		{{DISPLAYTITLE: Discrete ''q''-Hermite polynomials }}
			In mathematics, the '''discrete ''q''-Hermite polynomials''' are two closely related families ''h''<sub>''n''</sub>(''x'';''q'') and ''ĥ''<sub>''n''</sub>(''x'';''q'') of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], introduced by {{harvs\|txt\|last1=Al-Salam\|last2=Carlitz\|year=1965}}. {{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 discrete ''q''-Hermite polynomials are given in terms of [[basic hypergeometric function]]s and the [[Al-Salam–Carlitz polynomials]] by
			:<math>\displaystyle h_n(x;q)=q^{\binom{n}{2}}{}_2\phi_1(q^{-n},x^{-1};0;q,-qx) = x^n{}_2\phi_0(q^{-n},q^{-n+1};;q^2,q^{2n-1}/x^2) = U_n^{(-1)}(x;q) </math>
			:<math>\displaystyle \hat h_n(x;q)=i^{-n}q^{-\binom{n}{2}}{}_2\phi_0(q^{-n},ix;;q,-q^n) = x^n{}_2\phi_1(q^{-n},q^{-n+1};0;q^2,-q^{2}/x^2) = i^{-n}V_n^{(-1)}(ix;q) </math>
			and are related by
			:<math>h_n(ix;q^{-1}) = i^n\hat h_n(x;q)</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=Berg \| first1=Christian \| last2=Ismael \| first2=Mourad \| year=1994 \| title=Q-Hermite Polynomials and Classical Orthogonal Polynomials [http://arxiv.org/pdf/math/9405213v1.pdf]}}
			*{{Citation \| last1=Al-Salam \| first1=W. A. \| last2=Carlitz \| first2=L. \| author2-link=Leonard_Carlitz \| title=Some orthogonal q-polynomials \| doi=10.1002/mana.19650300105 \| mr=0197804 \| year=1965 \| journal=[[Mathematische Nachrichten]] \| issn=0025-584X \| volume=30 \| pages=47–61}}
			*{{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

2011-09-05T08:02:04Z

Various citation cleanup (identifiers mostly) using AWB

New page

Medical Light Therapist Leigh Corredor from La Ronge, enjoys to spend time bonsai trees, ganhando dinheiro na internet and crafts. During the recent month or two has visited to spots for example Monastery of the Hieronymites and Tower of Belém in Lisbon.<br><br>Here is my web page: [http://comoconseguirdinheiro.comoganhardinheiro101.com ganhar dinheiro]

Sieved ultraspherical polynomials - Revision history

en>Hakamiso: the names cannot be easily linked that way, and it makes the article confusing.

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