Carl Gustav Jacob Jacobi | EPFL Graph Search

Carl Gustav Jacob Jacobi (dʒəˈkoʊbi; jaˈkoːbi; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants, and number theory. His name is occasionally written as Carolus Gustavus Iacobus Iacobi in his Latin books, and his first name is sometimes given as Karl. Jacobi was born of Ashkenazi Jewish parentage in Potsdam on 10 December 1804. He was the second of four children of banker Simon Jacobi. His elder brother Moritz von Jacobi would also become known later as an engineer and physicist. He was initially home schooled by his uncle Lehman, who instructed him in the classical languages and elements of mathematics. In 1816, the twelve-year-old Jacobi went to the Potsdam Gymnasium, where students were taught all the standard subjects: classical languages, history, philology, mathematics, sciences, etc. As a result of the good education he had received from his uncle, as well as his own remarkable abilities, after less than half a year Jacobi was moved to the senior year despite his young age. However, as the University would not accept students younger than 16 years old, he had to remain in the senior class until 1821. He used this time to advance his knowledge, showing interest in all subjects, including Latin, Greek, philology, history and mathematics. During this period he also made his first attempts at research, trying to solve the quintic equation by radicals. In 1821 Jacobi went to study at Berlin University, where he initially divided his attention between his passions for philology and mathematics. In philology he participated in the seminars of Böckh, drawing the professor's attention with his talent. Jacobi did not follow a lot of mathematics classes at the time, finding the level of mathematics taught at Berlin University too elementary. He continued, instead, with his private study of the more advanced works of Euler, Lagrange and Laplace.

A generalization of the Wiener rational basis functions on infinite intervals: Part I-derivation and properties

Jan Sickmann Hesthaven

We formulate and derive a generalization of an orthogonal rational-function basis for spectral expansions over the infinite or semi-infinite interval. The original functions, first presented by Wiener, are a mapping and weighting of the Fourier basis to th ...

American Mathematical Society2011