  The use of the Dunkl derivative, which is defined by a combination of the
difference-differential and reflection operator, allows the classification of
the solutions according to even and odd solutions. Recently, we considered the
Dunkl formalism to investigate the Bose-Einstein condensation of an ideal Bose
gas confined in a gravitational field. In this work, we address a similar
problem and examine an ideal Bose gas trapped by a three-dimensional harmonic
oscillator within the Dunkl formalism. To this end, we derive an analytic
expression for the critical temperature of the N particle system, discuss its
value at large-N limit and finally derive and compare the ground state
population with the usual case result. In addition, we explore two thermal
quantities, namely the Dunkl-internal energy and the Dunkl-heat capacity
functions. The Wigner parameter of the Dunkl formalism can be successfully used
to obtain a better agreement between experimental and theoretical results.
