Jacobi, C. G. J. On a special kind of algebraic functions that arise from developing the function \((1-2xz+z^2)^{1/2}\). (Ueber eine besondere Gattung algebraischer Functionen, die aus der Entwicklung der Function \((1-2xz+z^2)^{1/2}\) entstehen.) (German) ERAM 002.0059cj J. Reine Angew. Math. 2, 223-226 (1827). Jacobi studies the polynomials \(X_n(x)\) introduced in 1784 by Legendre and proves the “fundamental property” \(X_n = 2^{-n} \cdot \frac{\partial^n(x^2-1)^n}{n! \partial x^n}\). Reviewer: Franz Lemmermeyer (Jagstzell) (2015) MSC: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) Keywords:Legendre polynomials PDFBibTeX XMLCite \textit{C. G. J. Jacobi}, J. Reine Angew. Math. 2, 223--226 (1827; ERAM 002.0059cj) Full Text: DOI EuDML