Connections between Romanovski and other polynomials

✍ Scribed by Hans J. Weber

• Book ID: 111488395
• Publisher: SP Versita
• Year: 2007
• Tongue: English
• Weight: 239 KB
• Volume: 5
• Category: Article
• ISSN: 1895-1074
• DOI: 10.2478/s11533-007-0014-4

✦ Synopsis

A connection between Romanovski polynomials and those polynomials that solve the onedimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.