### Abstract

The Hahn and Meixner polynomials belonging to the classical orthogonal polynomials of a discrete variable are analytically continued in the complex plane both in variable and parameter. This leads to the origination of two systems of real polynomials orthogonal with respect to a continuous measure. The Meixner polynomials of an imaginary argument obtained in this manner turned out to be known in the literature as the Pollaczek polynomials. The orthogonality relation for the Hahn polynomials with respect to a continuous measure is apparently new. A close connection between the Hahn polynomials of an imaginary argument and representations of the Lorentz group SO(3,1) is considered.

Original language | English (US) |
---|---|

Article number | 014 |

Pages (from-to) | 1583-1596 |

Number of pages | 14 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 18 |

Issue number | 10 |

DOIs | |

State | Published - 1985 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*18*(10), 1583-1596. [014]. https://doi.org/10.1088/0305-4470/18/10/014

**The Hahn and Meixner polynomials of an imaginary argument and some of their applications.** / Atakishiyev, N. M.; Suslov, Sergei.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 18, no. 10, 014, pp. 1583-1596. https://doi.org/10.1088/0305-4470/18/10/014

}

TY - JOUR

T1 - The Hahn and Meixner polynomials of an imaginary argument and some of their applications

AU - Atakishiyev, N. M.

AU - Suslov, Sergei

PY - 1985

Y1 - 1985

N2 - The Hahn and Meixner polynomials belonging to the classical orthogonal polynomials of a discrete variable are analytically continued in the complex plane both in variable and parameter. This leads to the origination of two systems of real polynomials orthogonal with respect to a continuous measure. The Meixner polynomials of an imaginary argument obtained in this manner turned out to be known in the literature as the Pollaczek polynomials. The orthogonality relation for the Hahn polynomials with respect to a continuous measure is apparently new. A close connection between the Hahn polynomials of an imaginary argument and representations of the Lorentz group SO(3,1) is considered.

AB - The Hahn and Meixner polynomials belonging to the classical orthogonal polynomials of a discrete variable are analytically continued in the complex plane both in variable and parameter. This leads to the origination of two systems of real polynomials orthogonal with respect to a continuous measure. The Meixner polynomials of an imaginary argument obtained in this manner turned out to be known in the literature as the Pollaczek polynomials. The orthogonality relation for the Hahn polynomials with respect to a continuous measure is apparently new. A close connection between the Hahn polynomials of an imaginary argument and representations of the Lorentz group SO(3,1) is considered.

UR - http://www.scopus.com/inward/record.url?scp=0001264845&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001264845&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/18/10/014

DO - 10.1088/0305-4470/18/10/014

M3 - Article

AN - SCOPUS:0001264845

VL - 18

SP - 1583

EP - 1596

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 10

M1 - 014

ER -