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

Soon Yi Kang, Sung Geun Lim, Jaebum Sohn

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2005 Jul 1

Bibliographical note

Funding Information:
* Corresponding author. E-mail address: (S.-Y. Kang). 1 Supported by Korea Research Foundation Grant (KRF-2004-015-C00005).

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'The continuous symmetric Hahn polynomials found in Ramanujan's lost notebook'. Together they form a unique fingerprint.

Cite this