Related papers: Series with Hermite Polynomials and Harmonic Numbe…

Comment on ``Gibbs Sampling, Exponential Families and Orthogonal Polynomials'' [arXiv:0808.3852]

We propose and study the properties of a set of polynomials $M_{n\alpha, H\ }^{s}(z)$, $C_{n\alpha, H}^{s}(z)$ $W_{n\alpha, H}^{s}(z)$ with $n,s\in N$ $;\alpha =\pm 1;$and where $H$ stands for Hermite ; the ''root '' polynomial >.These…

The continuous big $q$-Hermite polynomials are shown to realize a basis for a representation space of an extended $q$-oscillator algebra. An expansion formula is algebraically derived using this model.

In this note we explicit the notion of Hermite interpolant of a multivariate symmetric polynomial, generalizing the notion of Lagrange interpolant to the case when there are roots coalescence, an extension of the results on the symmetric…

In this paper we use the equivariant version of factorization homology constructed using the parametrized higher category theory and show that it can be used to describe the results used in the series of papers.

A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical…

We show how the combined use of the generating function method and of the theory of multivariable Hermite polynomials is naturally suited to evaluate integrals of gaussian functions and of multiple products of Hermite polynomials.

A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…

In this paper we collect some results about arithmetic progressions of higher order, also called polynomial sequences. Those results are applied to $(m,q)$-isometric maps.

In this paper we prove some new series for $1/\pi$ as well as related congruences. We also raise several new kinds of series for $1/\pi$ and present some related conjectural congruences involving representations of primes by binary…

Comment on ``Gibbs Sampling, Exponential Families, and Orthogonal Polynomials'' [arXiv:0808.3852]

We characterize the sets of solvability for Hermite multivariate interpolation problems when the sum of multiplicities is at most $2n + 2$, with $n$ the degree of the polynomial space. This result extends an earlier theorem (2000) by one of…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

We provide an explicit formula for the coefficient polynomials of a Hermite diagonal differential operator. The analysis of the zeros of these coefficient polynomials yields the characterization of generalized Hermite multiplier sequences…

In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.

In this paper, we give new identities involving Phillips q-Bernstein polynomials and we derive some interesting properties of q-Berstein polynomials associated with q-Stirling numbers and q-Bernoulli polynomials.

The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equivalent to several well-known characterizations appearing in the…

We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…

We present a relationship between the generalized hyperharmonic numbers and the poly-Bernoulli polynomials, motivated from the connections between harmonic and Bernoulli numbers. This relationship yields numerous identities for the…

In this work, we give the power series solutions around an ordinary point, in the case of variable coefficients, homogeneous sequential linear conformable fractional differential equations of order 2\alpha. Further, we introduce the…