1. CJM 2010 (vol 63 pp. 181)
 Ismail, Mourad E. H.; Obermaier, Josef

Characterizations of Continuous and Discrete $q$Ultraspherical Polynomials
We characterize the continuous $q$ultraspherical polynomials in
terms of the special form of the coefficients in the expansion
$\mathcal{D}_q P_n(x)$ in the basis $\{P_n(x)\}$, $\mathcal{D}_q$
being the AskeyWilson divided difference operator. The polynomials
are assumed to be symmetric, and the connection coefficients
are multiples of the reciprocal of the square of the $L^2$ norm of
the polynomials. A similar characterization is given for the discrete
$q$ultraspherical polynomials. A new proof of the evaluation of
the connection coefficients for big $q$Jacobi polynomials is given.
Keywords:continuous $q$ultraspherical polynomials, big $q$Jacobi polynomials, discrete $q$ultra\spherical polynomials, AskeyWilson operator, $q$difference operator, recursion coefficients Categories:33D45, 42C05 

2. CJM 2007 (vol 59 pp. 1223)
 Buraczewski, Dariusz; Martinez, Teresa; Torrea, José L.

CalderÃ³nZygmund Operators Associated to Ultraspherical Expansions
We define the higher order Riesz transforms and the LittlewoodPaley
$g$function
associated to the differential operator $L_\l f(\theta)=f''(\theta)2\l\cot\theta
f'(\theta)+\l^2f(\theta)$. We prove that these operators are
Calder\'{o}nZygmund operators in the homogeneous type space
$((0,\pi),(\sin t)^{2\l}\,dt)$. Consequently, $L^p$ weighted,
$H^1L^1$ and $L^\inftyBMO$ inequalities are obtained.
Keywords:ultraspherical polynomials, CalderÃ³nZygmund operators Categories:42C05, 42C15frcs 

3. CJM 2002 (vol 54 pp. 709)
 Ismail, Mourad E. H.; Stanton, Dennis

$q$Integral and Moment Representations for $q$Orthogonal Polynomials
We develop a method for deriving integral representations of certain
orthogonal polynomials as moments. These moment representations are
applied to find linear and multilinear generating functions for
$q$orthogonal polynomials. As a byproduct we establish new
transformation formulas for combinations of basic hypergeometric
functions, including a new representation of the $q$exponential
function $\mathcal{E}_q$.
Keywords:$q$integral, $q$orthogonal polynomials, associated polynomials, $q$difference equations, generating functions, AlSalamChihara polynomials, continuous $q$ultraspherical polynomials Categories:33D45, 33D20, 33C45, 30E05 

4. CJM 1997 (vol 49 pp. 520)
 Ismail, Mourad E. H.; Stanton, Dennis

Classical orthogonal polynomials as moments
We show that the Meixner, Pollaczek, MeixnerPollaczek, the continuous
$q$ultraspherical polynomials and AlSalamChihara polynomials, in
certain normalization, are moments of probability measures. We use
this fact to derive bilinear and multilinear generating functions for
some of these polynomials. We also comment on the corresponding formulas
for the Charlier, Hermite and Laguerre polynomials.
Keywords:Classical orthogonal polynomials, \ACP, continuous, $q$ultraspherical polynomials, generating functions, multilinear, generating functions, transformation formulas, umbral calculus Categories:33D45, 33D20, 33C45, 30E05 
