Displaying similar documents to “Linearization of Arbitrary products of classical orthogonal polynomials”

[unknown]

D. Mangeron, A. M. Krall, D. L. Fernández (1983)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Similarity:

[unknown]

D. Mangeron, A. M. Krall, D. L. Fernández (1983)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Similarity:

Existence and reduction of generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials

Luis M. Navas, Francisco J. Ruiz, Juan L. Varona (2019)

Archivum Mathematicum

Similarity:

One can find in the mathematical literature many recent papers studying the generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, defined by means of generating functions. In this article we clarify the range of parameters in which these definitions are valid and when they provide essentially different families of polynomials. In particular, we show that, up to multiplicative constants, it is enough to take as the “main family” those given by 2 λ e t + 1 α e x t = ∑ n = 0 ∞ ℰ n ( α ) ( x ; λ ) t n n ! , λ ∈ ℂ ∖ { - 1 } , and as an “exceptional...

Operators preserving orthogonality of polynomials

Francisco Marcellán, Franciszek Szafraniec (1996)

Studia Mathematica

Similarity:

Let S be a degree preserving linear operator of ℝ[X] into itself. The question is if, preserving orthogonality of some orthogonal polynomial sequences, S must necessarily be an operator of composition with some affine function of ℝ. In [2] this problem was considered for S mapping sequences of Laguerre polynomials onto sequences of orthogonal polynomials. Here we improve substantially the theorems of [2] as well as disprove the conjecture proposed there. We also consider the same questions...