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Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The f
Both volumes of classic text on trigonometric series, with a foreword by Robert Fefferman.
Collected papers of Salomon Bochner, American mathematician, known for work in mathematical analysis, probability theory and differential geometry.
In this present paper we will develop some theorems concerning the degree of convergence of certain series, in particular a Fourier's series, a Legendre's series, and a series of Bessel's functions. Before proceeding directly to the proof of these theorems, however, we will give some theorems showing the conditions under which the Fourier coefficients in the development of a function will converge to zero.