Results 21 to 30 of about 1,201 (100)

Recurrence relations of the multi-indexed orthogonal polynomials. VI. Meixner–Pollaczek and continuous Hahn types [PDF]

Journal of Mathematical Physics, 2020
In previous papers, we discussed the recurrence relations of the multi-indexed orthogonal polynomials of the Laguerre, Jacobi, Wilson, Askey–Wilson, Racah, and q-Racah types. In this paper, we explore those of the Meixner–Pollaczek and continuous Hahn types.
S. Odake
openaire   +3 more sources

Existence of a pair of new recurrence relations for the Meixner-Pollaczek polynomials

Tbilisi Mathematical Journal, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jafarov, E. I., Jafarova, A. M., Nagiyev, S. M.   +2 more
openaire   +4 more sources

Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators [PDF]

, 2016
We give explicit analytical expressions for the partition function of $U(N)_{k}\times U(N+M)_{-k}$ ABJ theory at weak coupling ($k\rightarrow \infty )$ for finite and arbitrary values of $N$ and $M$ (including the ABJM case and its mass-deformed generalization).
M. Tierz
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Exactly solvable discrete quantum mechanical systems and multi-indexed orthogonal polynomials of the continuous Hahn and Meixner–Pollaczek types [PDF]

Progress of Theoretical and Experimental Physics, 2019
Abstract We present new exactly solvable systems of the discrete quantum mechanics with pure imaginary shifts, whose physical range of coordinates is a whole real line. These systems are shape invariant and their eigenfunctions are described by the multi-indexed continuous Hahn and Meixner–Pollaczek orthogonal polynomials.
S. Odake
openaire   +4 more sources

Interlacing of zeros from different sequences of Meixner-Pollaczek, Pseudo-Jacobi and Continuous Hahn polynomials

Numerical Algorithms
Abstract In this paper we consider interlacing of the zeros of polynomials from different sequences $$\{p_n\}$$ { p n }
Jooste, Aletta, Jordaan, Kerstin
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Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme

Advances in Mathematical Physics, Volume 2009, Issue 1, 2009., 2009
In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three‐term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of ...
M. Bruschi, F. Calogero, R. Droghei, M. Lakshmanan   +3 more
wiley   +1 more source

Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics [PDF]

, 2006
The annihilation-creation operators $a^{(\pm)}$ are defined as the positive/negative frequency parts of the exact Heisenberg operator solution for the `sinusoidal coordinate'.
Andrews G. E., Ryu Sasaki, Satoru Odake
core   +4 more sources

Linearization coefficients for Sheffer polynomial sets via lowering operators

International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006
The lowering operator σ associated with a polynomial set {Pn} n≥0 is an operator not depending on n and satisfying the relation σPn = nPn−1. In this paper, we express explicitly the linearization coefficients for polynomial sets of Sheffer type using the corresponding lowering operators. We obtain some well‐known results as particular cases.
Y. Ben Cheikh, H. Chaggara
wiley   +1 more source

Multivariable Meixner, Krawtchouk, and Meixner–Pollaczek polynomials [PDF]

Journal of Mathematical Physics, 1989
A multivariable biorthogonal generalization of the Meixner, Krawtchouk, and Meixner–Pollaczek polynomials is presented. It is shown that these are orthogonal with respect to subspaces of lower degree and biorthogonal within a given subspace. The weight function associated with the Krawtchouk polynomials is the multivariate binomial distribution.
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Radial Bargmann representation for the Fock space of type B [PDF]

, 2016
Let $\nu_{\alpha,q}$ be the probability and orthogonality measure for the $q$-Meixner-Pollaczek orthogonal polynomials, which has appeared in \cite{BEH15} as the distribution of the $(\alpha,q)$-Gaussian process (the Gaussian process of type B) over the $
Asai N., Bożejko M., Chihara T. S., Hora A., Krystek A. D., Królak I., Marek Bożejko, Nobuhiro Asai, Saitoh N., Simon B., Takahiro Hasebe   +10 more
core   +3 more sources