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This work allowed us to establish some impossible cases as also to present a few families of such 2-orthogonal polynomial sequences. In this paper, we apply the symbolic setup proposed in [23] in order to enlighten us about further 2-orthogonal polynomial solutions of this problem. Concerning a general family inhere described, it is also proved its Hahn-classical character. Additionally, some functional identities are established.<\/jats:p>","DOI":"10.1007\/s11786-024-00583-0","type":"journal-article","created":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T08:01:31Z","timestamp":1716278491000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On a General Family of 2-Orthogonal Polynomial Eigenfunctions of a Third Order Differential Equation via Symbolic Computation"],"prefix":"10.1007","volume":"18","author":[{"given":"Teresa Augusta","family":"Mesquita","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,21]]},"reference":[{"key":"583_CR1","doi-asserted-by":"publisher","first-page":"730","DOI":"10.1007\/BF01180560","volume":"29","author":"S Bochner","year":"1929","unstructured":"Bochner, S.: \u00dcber Sturm-Liouvillesche polynomsysteme. Math. Zeit. 29, 730\u2013736 (1929)","journal-title":"Math. 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