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Josef Meixner: his life and his orthogonal polynomials

Paul L. Butzer, Tom H. Koornwinder

Abstract

This paper starts with a biographical sketch of the life of Josef Meixner. Then his motivations to work on orthogonal polynomials and special functions are reviewed. Meixner's 1934 paper introducing the Meixner and Meixner-Pollaczek polynomials is discussed in detail. Truksa's forgotten 1931 paper, which already contains the Meixner polynomials, is mentioned. The paper ends with a survey of the reception of Meixner's 1934 paper.

Josef Meixner: his life and his orthogonal polynomials

Abstract

This paper starts with a biographical sketch of the life of Josef Meixner. Then his motivations to work on orthogonal polynomials and special functions are reviewed. Meixner's 1934 paper introducing the Meixner and Meixner-Pollaczek polynomials is discussed in detail. Truksa's forgotten 1931 paper, which already contains the Meixner polynomials, is mentioned. The paper ends with a survey of the reception of Meixner's 1934 paper.

Paper Structure

This paper contains 12 sections, 35 equations.

Table of Contents

  1. Introduction
  2. Biographical notes
  3. Meixner's work in orthogonal polynomials and special functions: his motivations
  4. Meixner's introduction of the Meixner and Meixner-Pollaczek polynomials
  5. Case I
  6. Case II
  7. Case III
  8. Case IV
  9. Case V
  10. A predecessor, a missed class of polynomials and a rediscovery
  11. Case VI
  12. Follow-up of Meixner's 1934 paper