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

Soon Yi Kang, Sung Geun Lim, Jaebum Sohn

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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

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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