199.46.199.230 at 16:45, 31 July 2013

2013-07-31T16:45:57Z

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			In mathematics, the '''continuous dual Hahn polynomials''' are a family of [[orthogonal polynomials]] in the [[Askey scheme]] of hypergeometric orthogonal polynomials. They are defined in terms of [[generalized hypergeometric function]]s by
			:<math>S_n(x^2;a,b,c)= {}_3F_2(-n,a+ix,a-ix;a+b,a+c;1).\ </math>

			{{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.

	~~Bernie is what~~'~~s written on my birth certificate although it~~'~~s very not common history on my birth certificate. His friends say it~~'~~s unhealthy for him but what he loves doing is actually by play stone and he~~'~~ll be starting something else along from it. Meter reading exactly what I do in my~~ [~~http:~~/~~/www~~.~~Wonderhowto.com~~/~~search/day+job/ day job] but I~~'~~ve already signed another one. His family lives in Maine. I~~'~~ve been functioning~~ on ~~my website for days now~~. ~~Confirm it out here: https:~~/~~/www~~.~~youtube~~.~~com/watch?v~~=jZ-~~rP3WK7bo<br><br>Also visit my webpage ::~~ [~~https~~:~~//www~~.~~youtube~~.~~com/watch?v~~=~~jZ-rP3WK7bo web page~~]		Closely related polynomials include the [[dual Hahn polynomials]] ''R''<sub>''n''</sub>(''x'';γ,δ,''N''), the [[continuous Hahn polynomials]] ''p''<sub>''n''</sub>(''x'',''a'',''b'', {{overline\|''a''}}, {{overline\|''b''}}), and the [[Hahn polynomials]]. These polynomials all have ''q''-analogs with an extra parameter ''q'', such as the [[q-Hahn polynomials]] ''Q''<sub>''n''</sub>(''x'';α,β, ''N'';''q''), and so on.

			==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==

			*[[Wilson polynomials]] are a generalization of continuous dual Hahn polynomials

			==References==

			*{{Citation \| last1=Hahn \| first1=Wolfgang \| title=Über Orthogonalpolynome, die q-Differenzengleichungen genügen \| doi=10.1002/mana.19490020103 \| mr=0030647 \| year=1949 \| journal=Mathematische Nachrichten \| issn=0025-584X \| volume=2 \| pages=4–34}}
			*{{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=18.19\|title=Hahn Class: Definitions\|first=Tom H. \|last=Koornwinder\|first2=Roderick S. C.\|last2= Wong\|first3=Roelof \|last3=Koekoek\|\|first4=René F. \|last4=Swarttouw}}

			[[Category:Special hypergeometric functions]]
			[[Category:Orthogonal polynomials]]

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2012-08-13T02:55:13Z

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Bernie is what's written on my birth certificate although it's very not common history on my birth certificate. His friends say it's unhealthy for him but what he loves doing is actually by play stone and he'll be starting something else along from it. Meter reading exactly what I do in my [http://www.Wonderhowto.com/search/day+job/ day job] but I've already signed another one. His family lives in Maine. I've been functioning on my website for days now. Confirm it out here: https://www.youtube.com/watch?v=jZ-rP3WK7bo<br><br>Also visit my webpage :: [https://www.youtube.com/watch?v=jZ-rP3WK7bo web page]

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199.46.199.230 at 16:45, 31 July 2013

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