4.9 q-Meixner-Pollaczek

Continuous q-Hahn q-Meixner-Pollaczek.

  
The q-Meixner-Pollaczek polynomials defined by (3.9.1) simply follow from the continuous q-Hahn polynomials if we set d = a and b = c = 0 in the definition (3.4.1) of the continuous q-Hahn polynomials :

q-Meixner-Pollaczek Continuous q-ultraspherical / Rogers.

    
If we take and in the definition (3.9.1) of the q-Meixner-Pollaczek polynomials we obtain the continuous q-ultraspherical (or Rogers) polynomials given by (3.10.15) :

q-Meixner-Pollaczek Continuous q-Laguerre.

  
If we take , and in the definition (3.9.1) of the q-Meixner-Pollaczek polynomials we obtain the continuous q-Laguerre polynomials given by (3.19.1) :




Last modified on July 7, 1998