Presidents of the United States on U.S. postage stamps back several Confederate advances. During his military service he was wounded on five separate incidents. James Abram Garfield (November 19, 1831September 19, 1881) was the 20th President of the United States. An assassin's bullet ended his life and presidency and cut his time in office after serving only 200 days. He had a distinguished military background. Garfield served in the United States Army as a Major General, as a member of the U.S. House of Representatives, and as a member of the highly controversial Electoral Commission of 1876. He was the second U.S. President to be assassinated. Garfield was the
Eigenvalues and eigenvectors of the second derivative the kth Chebyshev polynomial of the 2nd kind. And combining with our Neumann boundary condition, we have A well-known formula relates the Chebyshev polynomials of the first kind, formula_81, to those of the second kind by Thus our eigenvalues solve The zeros of this polynomial are also known to be And thus Note that there are 2n + 1 of these values, but only the first n + 1 are unique. The (n + 1)th value gives us the zero vector as an eigenvector with eigenvalue 0, which is trivial. This can be seen by returning to the original recurrence.