Related papers: A generating function for Hermite polynomials in c…
The operational calculus associated with Hermite numbers has been shown to be an effective tool for simplifying the study of special functions. Within this context, Hermite polynomials have been viewed as Newton binomials, with the…
This paper is devoted to the explicit computation of generating series for the connection coefficients of two commutative subalgebras of the group algebra of the symmetric group, the class algebra and the double coset algebra. As shown by…
The subject of this paper are polynomials in multiple non-commuting variables. For polynomials of this type orthogonal with respect to a state, we prove a Favard-type recursion relation. On the other hand, free Sheffer polynomials are a…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and…
We give integral representations for multiple Hermite and multiple Hermite polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.
In this note we investigate mixed partitions with extra condition on the sizes of the blocks. We give a general formula and the generating function. We consider in more details a special case, determining the generating functions, some…
We discuss a method for computing the generating function for the multiplicity distribution in field theories with strong time dependent external sources. At leading order, the computation of the generating function reduces to finding a…
Lin and Chang gave a generating function of convex polyominoes with an $m+1$ by $n+1$ minimal bounding rectangle. Gessel showed that their result implies that the number of such polyominoes is $$ \frac{m+n+mn}{m+n}{2m+2n\choose…
This article develops the algebraic structure that results from the $\theta$-commutator $\alpha \beta - e^{i \theta} \beta \alpha = 1 $ that provides a continuous interpolation between the Clifford and Heisenberg algebras. We first…
In this paper, we discuss sums of powers of the positive integers and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and…
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…
We investigate Dirichlet-type series generated by representation functions that count the number of ways an integer can be expressed as a sum of 'k' signed higher even powers. By combining generalized theta generating functions with a…
We explicitly construct a Hamiltonian whose exact eigenfunctions are the generalized Laguerre functions. Moreover, we present the related raising and lowering operators. We investigate the corresponding coherent states by adopting the…
A general group element for the fundamental representation of SU(3) is expressed as a second order polynomial in the hermitian generating matrix H, with coefficients consisting of elementary trigonometric functions dependent on the sole…
In even-dimensional Euclidean space for integer powers of the Laplacian greater than or equal to the dimension divided by two, a fundamental solution for the polyharmonic equation has logarithmic behavior. We give two approaches for…
We are continuing here the study of generalized coherent states of Barut-Girardello type for the oscillator-like systems connected with the given set of orthogonal polynomials. In this work we construct the family of coherent states…
Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that various classes of coherent states such as the canonical coherent states, pure squeezed states, fermionic coherent states can be defined…
Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes…
A theorem of Meinardus provides asymptotics of the number of weighted partitions under certain assumptions on associated ordinary and Dirichlet generating functions. The ordinary generating functions are closely related to Euler's…