|
|
| Line 1: |
Line 1: |
| {{DISPLAYTITLE: ''q''-Bessel polynomials }}
| | Im Glenna and was born on 14 September 1990. My hobbies are Trainspotting and Exhibition Drill.<br><br>Feel free to visit my blog post :: [http://tinyurl.com/m6ep7fh ugg sale] |
| In mathematics, the '''''q''-Bessel 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]]
| |
Revision as of 21:32, 2 March 2014
Im Glenna and was born on 14 September 1990. My hobbies are Trainspotting and Exhibition Drill.
Feel free to visit my blog post :: ugg sale