Abstract
Let R = ( - ∞ , ∞ ) and let w ρ ( x ) ≔ | x | ρ exp ( - Q ( x ) ) , where ρ > - 1 2 and Q ( x ) ∈ C 2 : R → R + = [ 0 , ∞ ) is an even function. In this paper we consider the properties of the orthonormal polynomials with respect to the weight w ρ 2 ( x ) , obtaining bounds on the orthonormal polynomials and spacing on their zeros. Moreover, we estimate A n ( x ) and B n ( x ) defined in Section 4, which are used in representing the derivative of the orthonormal polynomials with respect to the weight w ρ 2 ( x ) .
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