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| In mathematics, the '''Hahn–Exton q-Bessel function''' or the '''third [[Jackson q-Bessel function]]''' is a [[q-analog|''q''-analog]] of the [[Bessel function]], introduced by {{harvs|txt|last=Hahn|authorlink=Wolfgang Hahn|year=1953}} in a special case and by {{harvs|txt|last=Exton|authorlink=Harold Exton|year=1983}} in general.
| | My name is Alissa Gatenby but everybody calls me Alissa. I'm from France. I'm studying at the university (3rd year) and I play the Lap Steel Guitar for 6 years. Usually I choose music from my famous films :). <br>I have two sister. I love Hiking, watching movies and Geocaching.<br><br>Feel free to surf to my webpage ... [http://tinyurl.com/m28vwqy http://tinyurl.com/m28vwqy] |
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| The Hahn–Exton ''q''-Bessel function is given by
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| :<math> J_\nu^{(3)}(x;q) = \frac{x^\nu(q^{\nu+1};q)_\infty}{(q;q)_\infty} \sum_{k\ge 0}\frac{(-1)^kq^{k(k+1)/2}x^{2k}}{(q^{\nu+1};q)_k(q;q)_k} </math> | |
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| ==References==
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| *{{Citation | last1=Exton | first1=Harold | title=q-hypergeometric functions and applications | url=http://books.google.com/books?id=3kHvAAAAMAAJ | publisher=Ellis Horwood Ltd. | location=Chichester | series=Ellis Horwood Series: Mathematics and its Applications | isbn=978-0-85312-491-7 | mr=MR708496 | year=1983}}
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| *{{Citation | last1=Hahn | first1=Wolfgang | authorlink=Wolfgang Hahn | title=Die mechanische Deutung einer geometrischen Differenzengleichung | language=German | doi=10.1002/zamm.19530330811 | zbl=0051.15502 | year=1953 | journal=Zeitschrift für Angewandte Mathematik und Mechanik | issn=0044-2267 | volume=33 | pages=270–272}}
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| *{{citation|first=M. E. H.|last= Ismail|title= Some Properties of Jacksons Third q-Bessel Function|series=preprint|year=2003}}
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| *{{Citation | last1=Swarttouw | first1=René F. | title=An addition theorem and some product formulas for the Hahn-Exton q-Bessel functions | doi=10.4153/CJM-1992-052-6 | mr=1178574 | year=1992 | journal=[[Canadian Journal of Mathematics]] | issn=0008-414X | volume=44 | issue=4 | pages=867–879}}
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| {{DEFAULTSORT:Hahn-Exton q-Bessel function}}
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| [[Category:Special functions]]
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| [[Category:Q-analogs]]
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Latest revision as of 07:52, 10 May 2014
My name is Alissa Gatenby but everybody calls me Alissa. I'm from France. I'm studying at the university (3rd year) and I play the Lap Steel Guitar for 6 years. Usually I choose music from my famous films :).
I have two sister. I love Hiking, watching movies and Geocaching.
Feel free to surf to my webpage ... http://tinyurl.com/m28vwqy