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.
Bibliographical noteFunding Information:
* Corresponding author. E-mail address: firstname.lastname@example.org (S.-Y. Kang). 1 Supported by Korea Research Foundation Grant (KRF-2004-015-C00005).
All Science Journal Classification (ASJC) codes
- Applied Mathematics