Hahn–Exton q-Bessel fonksiyonu

Matematikte, Hahn–Exton q-Bessel fonksiyonu veya üç Jackson q-Bessel fonksiyonu özel bir durumdur ve genel olarak Exton (1983) ta Hahn Hahn (1953) tarafından tanıtıldı Exton (1983) genelledi,Bessel fonksiyonu'nun bir[[q-analog|'udur. Hahn–Exton q-Bessel fonksiyonu olarak verilen ifade

${\displaystyle J_{\nu }^{(3)}(x;q)={\frac {x^{\nu }(q^{\nu +1};q)_{\infty }}{(q;q)_{\infty }}}\sum _{k\geq 0}{\frac {(-1)^{k}q^{k(k+1)/2}x^{2k}}{(q^{\nu +1};q)_{k}(q;q)_{k}}}}$

Ayrıca bakınız

• Matematiksel fonksiyonların listesi

Kaynakça

• Exton, Harold (1983), q-hypergeometric functions and applications, Ellis Horwood Series: Mathematics and its Applications, Chichester: Ellis Horwood Ltd., ISBN 978-0-85312-491-7, MR MR708496, http://books.google.com/books?id=3kHvAAAAMAAJ 
• Hahn, Wolfgang (1953), "Die mechanische Deutung einer geometrischen Differenzengleichung" (German), Zeitschrift für Angewandte Mathematik und Mechanik 33: 270–272, DOI:10.1002/zamm.19530330811, ISSN 0044-2267, Zbl 0051.15502 
• Ismail, M. E. H. (2003), Some Properties of Jacksons Third q-Bessel Function, preprint 
• Swarttouw, René F. (1992), "An addition theorem and some product formulas for the Hahn-Exton q-Bessel functions", Canadian Journal of Mathematics 44 (4): 867–879, DOI:10.4153/CJM-1992-052-6, ISSN 0008-414X, MR 1178574