The continuous symmetric Hahn polynomials found in Ramanujan's lost notebook

Soon Yi Kang, Sung Geun Lim, Jaebum Sohn

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Askey and Wilson found 3F2 Hahn polynomials which are orthogonal with respect to a positive absolutely continuous weight function. More than a half century earlier, Ramanujan recorded the Stieltjes transform of this weight function in terms of a continued fraction in his lost notebook. We provide two different proofs for this integration. One applies theories of the Hamburger moment problem. The other uses elementary integration techniques and a couple of transformation formulas for hypergeometric functions.

Original languageEnglish
Pages (from-to)153-166
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume307
Issue number1
DOIs
Publication statusPublished - 2005 Jul 1

Fingerprint

Ramanujan's Lost Notebook
Hahn Polynomials
Symmetric Polynomials
Weight Function
Polynomials
Stieltjes Transform
Transformation Formula
Moment Problem
Hypergeometric Functions
Ramanujan
Absolutely Continuous
Continued fraction
Continuous Function

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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The continuous symmetric Hahn polynomials found in Ramanujan's lost notebook. / Kang, Soon Yi; Lim, Sung Geun; Sohn, Jaebum.

In: Journal of Mathematical Analysis and Applications, Vol. 307, No. 1, 01.07.2005, p. 153-166.

Research output: Contribution to journalArticle

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