Geodesic
$q$-integral representations of modified $q$-Bessel functions and $q$-Macdonald functions
Sbornik. Mathematics, Tome 188 (1997) no. 8, pp. 1235-1258

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The $q$-analogues of modified Bessel functions and Macdonald functions were defined in the previous paper of the authors as general solutions of certain second-order difference equations. Several representations of these functions based on the Jackson integral are presented. 
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     author = {M. A. Olshanetsky and V.-B. K. Rogov},
     title = {$q$-integral representations of modified $q${-Bessel} functions and $q${-Macdonald} functions},
     journal = {Sbornik. Mathematics},
     pages = {1235--1258},
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     volume = {188},
     number = {8},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_8_a8/}
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M. A. Olshanetsky; V.-B. K. Rogov. $q$-integral representations of modified $q$-Bessel functions and $q$-Macdonald functions. Sbornik. Mathematics, Tome 188 (1997) no. 8, pp. 1235-1258. http://geodesic.mathdoc.fr/item/SM_1997_188_8_a8/