Hahn–Exton q-Bessel function
Encyclopedia
In mathematics, the Hahn–Exton q-Bessel function or the third Jackson q-Bessel function
is a q-analog
of the Bessel function
, introduced by in a special case and by in general.
The Hahn–Exton q-Bessel function is given by
Jackson q-Bessel function
In mathematics, a Jackson q-Bessel function is one of the three q-analogs of the Bessel function introduced by...
is a q-analog
Q-analog
Roughly speaking, in mathematics, specifically in the areas of combinatorics and special functions, a q-analog of a theorem, identity or expression is a generalization involving a new parameter q that returns the original theorem, identity or expression in the limit as q → 1...
of the Bessel function
Bessel function
In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...
, introduced by in a special case and by in general.
The Hahn–Exton q-Bessel function is given by