Results 51 to 60 of about 1,331 (75)

New bounds on the Hermite polynomials [PDF]

arXiv, 2004
We shall establish two-side explicit inequalities, which are asymptotically sharp up to a constant factor, on the maximum value of $|H_k(x)| e^{-x^2/2},$ on the real axis, where $H_k$ are the Hermite polynomials.
arxiv  

Heat kernels of the discrete Laguerre operators. [PDF]

Lett Math Phys, 2021
Kostenko A.
europepmc   +1 more source

Alternative Orthogonal Polynomials [PDF]

arXiv, 2004
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences that are the result of the inverse orthogonalization procedure.
arxiv  

Asymptotic analysis of the Askey-scheme II: from Charlier to Hermite [PDF]

arXiv, 2005
We analyze the Hermite polynomials $H_{n}(\xi)$ and their zeros asymptotically as $n\to\infty,$ using the limit relation between the Charlier and Hermite polynomials. Our formulas involve some special functions and they yield very accurate approximations.
arxiv  

Parameter-based Fisher's information of orthogonal polynomials [PDF]

arXiv, 2006
The Fisher information of the classical orthogonal polynomials with respect to a parameter is introduced, its interest justified and its explicit expression for the Jacobi, Laguerre, Gegenbauer and Grosjean polynomials found.
arxiv  

The $M_{L}(z);C_{L}(z);W_{L}(z)$ associated Laguerre Polynomials [PDF]

arXiv, 2000
In a previous paper we deformed Hermite polynomials to three associated polynomials .Here we apply the same deformation to Laguerre polynomials .
arxiv  

Topics on Meixner families [PDF]

arXiv, 2008
We shed the light on the inter-connections between different characterizations leading to the classical, free and quantum Meixner families.
arxiv  

Special polynomials and elliptic integrals [PDF]

arXiv, 2009
We show that the use of generalized multivariable forms of Hermite polynomials provide an useful tool for the evaluation of families of elliptic type integrals often encountered in electrostatic and ...
arxiv  

Integrals Involving Associated Laguerre Polynomials [PDF]

arXiv, 2011
We present a closed-form expression for integrals involving product of associated Laguerre polynomials.
arxiv  

Symbolic calculus and integrals of Laguerre polynomials [PDF]

arXiv, 2012
An umbral type formalism is used to derive integrals involving products of Laguerre polynomials and other special functions.
arxiv