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{{DISPLAYTITLE: ''q''-Hahn polynomials}}
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{{see also|continuous q-Hahn polynomials|dual q-Hahn polynomials|continuous dual q-Hahn polynomials}}
In mathematics, the '''''q''-Hahn 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}}
This operation is a positive semidefinite inner product on the vector space of all polynomials, and is positive definite if the function α has an infinite number of points of growth. It induces a notion of orthogonality in the usual way, namely that two polynomials are orthogonal if their inner product is zero.
==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]]

Latest revision as of 08:01, 25 November 2014

If you want a bigger scare, start round trip or multiple destination trip with your "going there flight" nicely "coming home flight". She and I were going Calgary, Canada to Moscow, Russia and also Beijing, China to Calgary, Calgary. The tickets are no longer $3,200 now and were over $5,000 when we first looked a month ago.

Cape Town is amongst the capitals of South Africa; it's very talked-about for sightseeing opportunities it provides to its guests. As the fascinating city in the world has the possibility to captivate all it tourists, this an area of the world, located near the "Cape outstanding Hope" attributes a number of attractions for any boarding avion bucuresti londra low cost to Cape Town. When traveling on flights to Cape Town, you might want to consider all of the necessary traveler information during this fascinate town you live.

Next it's time for investigating online. This is where I almost always find least expensive flights. Go to one for this sites I listed above or another one you be familiar with.

It may be possible to find a hotel in Aspen that can make you at home and would pamper and cater for all your essentials. There are various hotels that provide comfort without the outrageous cost offered using the first class hotels. May also be spend on more luxurious hotels. Others opt to save the money for other travel premiums. It is option in the end.

If you wander in the inner districts of Shanghai, you arrived at what is known as Bund. This is the river bank of area of the city which was popular among commercial banks and business houses a early last century. There recently been major renovation along the river together with new walkway has been opened.

During a bitter winter months it tends turn out to be cold and wet which is even more often very snowy too. The average temperature in January and February is five qualifications. The snowfall within the city tends to be very heavy but it surely rarely last more than the usual couple of days. This city also tends to be really windy and it has an average wind speed of eighteen kilometers each hour. The average rainfall through the city is thirty-three inches and this can occur all year long.

It's brimming with the best views in this world. The rim, elevation 7,000 feet, is flat and thickly vegetated with pine forest. To get clear views, you need to the rim's advantages. Flying, its all sky above and Canyon lower.