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Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials

Marčoková, Mariana, Guldan, Vladimír (2017)

Proceedings of Equadiff 14

In this contribution we deal with classical Jacobi polynomials orthogonal with respect to different weight functions, their special cases - classical Legendre polynomials and generalized brothers of them. We derive expressions of generalized Legendre polynomials and generalized ultraspherical polynomials by means of classical Jacobi polynomials.

Closed-form expression for Hankel determinants of the Narayana polynomials

Marko D. Petković, Paul Barry, Predrag Rajković (2012)

Czechoslovak Mathematical Journal

We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana...

Complete Systems of Hermite Associated Functions

Rusev, Peter (2000)

Serdica Mathematical Journal

It is proved that if the increasing sequence kn n=0..∞ n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply connected subregion of CRthen the system of Hermite associated functions Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.

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