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

Askey and Wilson found F23 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.