On the Direct Limit from Pseudo Jacobi Polynomials to Hermite Polynomials

نویسندگان

چکیده

In this short communication, we present a new limit relation that reduces pseudo-Jacobi polynomials directly to Hermite polynomials. The proof of is based upon 2F1-type hypergeometric transformation formulas, which are applicable even and odd separately. This opens the way studying exactly solvable harmonic oscillator models in quantum mechanics terms

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials

A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn polynomials, little q-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey–Wilson to Wilson polynomials and from q-Racah to Racah polynomials ar...

متن کامل

On Hermite-hermite Matrix Polynomials

In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite ma...

متن کامل

On Pseudo Hermite Matrix Polynomials of Two Variables

Abstract. The main aim of this paper is to define a new polynomial, say, pseudo hyperbolic matrix functions, pseudo Hermite matrix polynomials and to study their properties. Some formulas related to an explicit representation, matrix recurrence relations are deduced, differential equations satisfied by them is presented, and the important role played in such a context by pseudo Hermite matrix p...

متن کامل

Szegö on Jacobi Polynomials

One of the interesting features in the development of analysis in the twentieth century is the remarkable growth, in various directions, of the theory of orthogonal functions. Two brilliant achievements on the threshold of this century—Fejér's paper on Fourier series and Fredholm's papers on integral equations—have been acting as a powerful inspiring source of attraction, inviting analysts to d...

متن کامل

From Hermite Polynomials to Multifractional Processes

We establish an invariance principle where the limit process is a Hermite-type process. We also prove that this limit process is multifractional. Our main result is a generalization of results from [6] and [11] to a multifractional setting. It also generalizes the main result of [3] to a non-Gaussian framework.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Mathematics

سال: 2021

ISSN: ['2227-7390']

DOI: https://doi.org/10.3390/math9010088