Articulos FC INSMAT

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Browsing Articulos FC INSMAT by Author "Juan Hernández"

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    A look at generalized degenerate Bernoulli and Euler matrices
    (2023-06-16) Juan Hernández
    In this paper, we consider the generalized degenerate Bernoulli/Euler polynomial matrices and study some algebraic properties for them. In particular, we focus our attention on some matrix-inversion formulae involving these matrices. Furthermore, we provide analytic properties for the so-called generalized degenerate Pascal matrix of the first kind, and some factorizations for the generalized degenerate Euler polynomial matrix.
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    Sequentially Ordered Sobolev Inner Product and Laguerre –Sobolev Polynomials
    (2023-04-20) Juan Hernández
    We study the sequence of polynomials {𝑆𝑛}𝑛≥0{𝑆𝑛}𝑛≥0 that are orthogonal with respect to the general discrete Sobolev-type inner product ⟨𝑓,𝑔⟩𝗌=∫𝑓(𝑥)𝑔(𝑥)𝑑𝜇(𝑥)+∑𝑁𝑗=1∑𝑑𝑗𝑘=0𝜆𝑗,𝑘𝑓(𝑘)(𝑐𝑗)𝑔(𝑘)(𝑐𝑗),⟨𝑓,𝑔⟩𝑠=∫𝑓(𝑥)𝑔(𝑥)𝑑𝜇(𝑥)+∑𝑗=1𝑁∑𝑘=0𝑑𝑗𝜆𝑗,𝑘𝑓(𝑘)(𝑐𝑗)𝑔(𝑘)(𝑐𝑗), where 𝜇𝜇 is a finite Borel measure whose support supp(𝜇)supp𝜇 is an infinite set of the real line, 𝜆𝑗,𝑘≥0𝜆𝑗,𝑘≥0, and the mass points 𝑐𝑖𝑐𝑖, 𝑖=1,…,𝑁𝑖=1,…,𝑁 are real values outside the interior of the convex hull of supp(𝜇)supp𝜇 (𝑐𝑖∈ℝ\𝐂ℎ(supp(𝜇))∘)𝑐𝑖∈𝑅\𝐶ℎ(supp(𝜇))∘). Under some restriction of order in the discrete part of ⟨•,•⟩𝗌⟨•,•⟩𝑠, we prove that 𝑆𝑛𝑆𝑛 has at least 𝑛−𝑑∗𝑛−𝑑* zeros on 𝐂ℎ(supp(𝜇))∘𝐶ℎ(supp𝜇)∘, being 𝑑∗𝑑* the number of terms in the discrete part of ⟨•,•⟩𝗌⟨•,•⟩𝑠. Finally, we obtain the outer relative asymptotic for {𝑆𝑛}{𝑆𝑛} in the case that the measure 𝜇𝜇 is the classical Laguerre measure, and for each mass point, only one order derivative appears in the discrete part of ⟨•,•⟩𝗌⟨•,•⟩𝑠.
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    Sequentially ordered Sobolevinner product and Laguerre – Sobolev polynomials
    (2023-04-20) Juan Hernández
    We study the sequence of polynomials {𝑆𝑛}𝑛≥0{𝑆𝑛}𝑛≥0 that are orthogonal with respect to the general discrete Sobolev-type inner product ⟨𝑓, 𝑔⟩{𝗌} = ∫ 𝑓(𝑥)𝑔(𝑥)𝑑𝜇(𝑥) + ∑ 𝑁𝑗=1 ∑ 𝑑𝑗𝑘=0 𝜆𝑗,𝑘𝑓(𝑘)(𝑐𝑗)𝑔(𝑘)(𝑐𝑗), ⟨𝑓, 𝑔⟩{𝑠} = ∫ 𝑓(𝑥)𝑔(𝑥)𝑑𝜇(𝑥) + ∑ 𝑗=1 𝑁 ∑ 𝑘=0 𝑑𝑗𝜆𝑗,𝑘𝑓(𝑘)(𝑐𝑗)𝑔(𝑘) (𝑐𝑗) where 𝜇𝜇 is a finite Borel measure whose support supp(𝜇) is an infinite set of the real line, 𝜆𝑗,𝑘≥0, and the mass points 𝑐𝑖, 𝑖=1,…,𝑁 are real values outside the interior of the convex hull of supp(𝜇)supp𝜇 (𝑐𝑖∈R\𝐂h(supp(𝜇))∘)𝑐𝑖∈𝑅\𝐶h(supp(𝜇))∘). Under some restriction of order in the discrete part of ⟨·,·⟩𝗌⟨·,·⟩𝑠, we prove that 𝑆𝑛𝑆𝑛 has at least 𝑛−𝑑∗𝑛−𝑑* zeros on 𝐂h(supp(𝜇))∘𝐶h(supp𝜇)∘, being 𝑑∗𝑑* the number of terms in the discrete part of ⟨·,·⟩𝗌⟨·,·⟩𝑠. Finally, we obtain the outer relative asymptotic for {𝑆𝑛}{𝑆𝑛} in the case that the measure 𝜇𝜇 is the classical Laguerre measure, and for each mass point, only one order derivative appears in the discrete part of ⟨·,·⟩𝗌⟨·,·⟩𝑠.
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    Some families of differential equations for jmultivariate hybrid special polynomials associated with Frobenius –Genocchi polynomials
    (2025-01-31) Juan Hernández
    This article introduces a new class of multi-variate Hermite-Frobenius-Genocchi polynomials and explores various characterizations of these polynomials. We examine their properties, including recurrence relations and shift operators. Using the factorization method, we derive differential, partial differential, and integrodifferential equations satisfied by these polynomials. Furthermore, we present the Volterra integral equation associated with these multi-variate Hermite-Frobenius-Genocchi polynomials, which improves our understanding and application of the factorization method in fields such as physics and engineering.
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    The monomiality principle applied to extensions of Apostol-Type hermite polynomials
    (2025) Juan Hernández
    In this research paper, we present a class of polynomials referred to as Apostol-type Hermite-Bernoulli/Euler polynomials , which can be given by the following generating function. for some particular values of and. Further, the summation formulae and determinant forms of these polynomials are derived. This novel family encompasses both the classical Appell-type polynomials and their noteworthy extensions. Our investigations heavily rely on generating function techniques, supported by illustrative examples to demonstrate the validity of our results. Furthermore, we introduce derivative and multiplicative operators, facilitating the definition of the Apostol-type Hermite-Bernoulli/Euler polynomials as a quasi-monomial set.