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The ultraspherical polynomials form a orthogonal system on 1=[-l,1] for the
measure dµ?(x)=(l_x2) ?dx for
The Gegenbauer’s multiplication formula shows that the Gegenbauer Kernel is stochastic. By means of the Gegenbauer Kernel we construct a Markov operator and by using the abstract result for a Markov Operators we prove its asymptotic stability for o ? ??½ This result will be
generalized for all ?? ½ by use of the
Harmonic analysis techniques.