The Jacobi polynomials, also known as hypergeometric polynomials, occur in the study of rotation groups and in the solution to the equations
of motion of the symmetric top. They are solutions to the Jacobi
differential equation, and give some other special named polynomials as special
cases. They are implemented in the Wolfram
Language as JacobiP[n,
a, b, z].

Abramowitz, M. and Stegun, I. A. (Eds.). "Orthogonal Polynomials." Ch. 22 in Handbook
of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, pp. 771-802, 1972.Andrews, G. E.; Askey,
R.; and Roy, R. "Jacobi Polynomials and Gram Determinants" and "Generating
Functions for Jacobi Polynomials." §6.3 and 6.4 in Special
Functions. Cambridge, England: Cambridge University Press, pp. 293-306,
1999.Iyanaga, S. and Kawada, Y. (Eds.). "Jacobi Polynomials."
Appendix A, Table 20.V in Encyclopedic
Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1480, 1980.Koekoek,
R. and Swarttouw, R. F. "Jacobi." §1.8 in The Askey-Scheme
of Hypergeometric Orthogonal Polynomials and its -Analogue. Delft, Netherlands: Technische Universiteit
Delft, Faculty of Technical Mathematics and Informatics Report 98-17, pp. 38-44,
1998.Roman, S. "The Theory of the Umbral Calculus I." J.
Math. Anal. Appl.87, 58-115, 1982.Szegö, G. "Jacobi
Polynomials." Ch. 4 in Orthogonal
Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., 1975.