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

Soon Yi Kang; Sung Geun Lim; Jaebum Sohn

doi:10.1016/j.jmaa.2004.12.054

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

Soon Yi Kang, Sung Geun Lim, Jaebum Sohn

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	153-166
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	307
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2004.12.054
Publication status	Published - 2005 Jul 1

Bibliographical note

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

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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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.",

author = "Kang, {Soon Yi} and Lim, {Sung Geun} and Jaebum Sohn",

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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