Related papers: Integrals Involving Associated Laguerre Polynomial…
This paper considers some integrals where the integrand comprises the log gamma function or the digamma function multiplied by exponential or trigonometric functions.
Motivated by the work of Prajapati \emph{et al.} \cite{PAA}, here we study some explicit form of the generalized Laguerre polynomials $L_{\lfloor\frac{n}{q}\rfloor}^{(\alpha,\beta)}(z)$, when $q=1$.
A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.
This short note investigates a number of index integrals of products of the Lommel functions $s_{\mu,\nu}(a)$ and uncovers an integral relationship. between this function and the Tchebyshev polynomials $T_{2n}(x)$.
This paper explores closed-form expressions for some polylogarithm integrals with integrands containing five parameters. These closed form expressions are given in terms of the Lerch transcendent function, which reduces, in some cases, to…
An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials $L^{(\alpha)}_n(z)$ are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic…
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 study the possibility of factoring a covariant distribution on reductive Lie algebras as finite sum of products of an invariant distribution by a covariant polynomial.
We present expressions for the coefficients which arise in asymptotic expansions of multiple integrals of Laplace type (the first term of which is known as Laplace's approximation) in terms of asymptotic series of the functions in the…
In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.
We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of…
We evaluate several arctangent and logarithmic integrals depending on a parameter. This provides a closed form summation of certain series and also gives integral and series representation of some classical constants.
In this paper we consider the strong asymptotic behavior of Laguerre polynomials in the complex plane. The leading behavior is well known from Perron and Mehler-Heine formulas, but higher order coefficients, which are important in the…
Certain computable polynomials are described whose leading coefficients are equal to multiplicities in the tensor product decomposition for representations of a Lie algebra of ADE type.
In a previous paper, we presented conjectures of the recurrence relations with constant coefficients for the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. In this paper we present a proof for the…
Using representations of sl(2,R) generators which yield associated Lame Hamiltonians we obtain new classes of elliptic potentials. We explicitly calculate eigenvalues and spectra for these potentials and construct the associated orthogonal…
We derive some identities and relations and extremal problems and minimization and Fourier development involving of integral Legendre polynomials.
This paper introduces a symbolic calculus-based approach for deriving closed-form expressions for the sums of arithmetic sequences. The method extends beyond constant-difference sequences to those with polynomially increasing steps,…
The analogous quaternionic polynomials of a class of bivariate orthogonal polynomials (arXiv: 1502.07256, 2014) introduced. The ladder operators for these quaternionic polynomials also studied. For the quaternionic case, the ladder…
By means of a modified hypervirial theorem we derive simple expressions for the integrals of products of Airy functions. Present results contain earlier ones as particular cases.