Jacobi, Karl Gustav Jakob

Born Dec. 10, 1804, in Potsdam; died Feb. 18, 1851, in Berlin. German mathematician. Member of the Berlin Academy of Sciences (1836); honorary member of the St. Petersburg Academy of Sciences (1833; corresponding member, 1830). Brother of B. S. Iakobi.

Jacobi was one of the founders of the theory of elliptic functions. He introduced and studied the theta functions and some other transcendental functions. He made discoveries in number theory, algebra, the calculus of variations, integral calculus, and the theory of differential equations. Jacobi investigated the differential equations of dynamics, for which he suggested several new methods of solution. He brought into use functional determinants and pointed out their role in the change of variables in multiple integrals and in the solution of partial differential equations (see). Jacobi investigated a class of orthogonal polynomials, now called Jacobi polynomials, that are generalizations of Legendre polynomials.