Displaying similar documents to “Identity-type functions and polynomials.”

On block recursions, Askey's sieved Jacobi polynomials and two related systems

Bernarda Aldana, Jairo Charris, Oriol Mora-Valbuena (1998)

Colloquium Mathematicae

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Two systems of sieved Jacobi polynomials introduced by R. Askey are considered. Their orthogonality measures are determined via the theory of blocks of recurrence relations, circumventing any resort to properties of the Askey-Wilson polynomials. The connection with polynomial mappings is examined. Some naturally related systems are also dealt with and a simple procedure to compute their orthogonality measures is devised which seems to be applicable in many other instances.

Connections between Romanovski and other polynomials

Hans Weber (2007)

Open Mathematics

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A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.

On some generalized Sister Celine’s polynomials

Mumtaz Ahmad Khan, Ajay Kumar Shukla (1999)

Czechoslovak Mathematical Journal

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Certain generalizations of Sister Celine’s polynomials are given which include most of the known polynomials as their special cases. Besides, generating functions and integral representations of these generalized polynomials are derived and a relation between generalized Laguerre polynomials and generalized Bateman’s polynomials is established.

On certain generalized q-Appell polynomial expansions

Thomas Ernst (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol–Bernoulli and Apostol–Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials...