4.24 Al-Salam-Carlitz I

Big q-Laguerre Al-Salam-Carlitz I.

  
If we set and in the definition (3.11.1) of the big q-Laguerre polynomials and take the limit we obtain the Al-Salam-Carlitz I polynomials given by (3.24.1) :

Dual q-Krawtchouk Al-Salam-Carlitz I.

  
If we set in the definition (3.17.1) of the dual q-Krawtchouk polynomials and take the limit we simply obtain the Al-Salam-Carlitz I polynomials given by (3.24.1) :

Note that .

Al-Salam-Carlitz I Discrete q-Hermite I.

   
The discrete q-Hermite I polynomials defined by (3.28.1) can easily be obtained from the Al-Salam-Carlitz I polynomials given by (3.24.1) by the substitution a = -1 :




Last modified on July 7, 1998