Web7 de mar. de 2011 · Weierstrass found an analogous function in 1875. The function is the limit of the ones graphed as .; Bolzano discovered this continuous but nowhere differentiable function before 1831 but these investigations were not published until 1930. Web1 Answer. Sorted by: 1. Your function is a Weierstrass function, which are of the form. W ( x) = ∑ k = 0 ∞ a k cos ( b n π x) Your function is of this form with a = 1 2 and b = 3, since then W ( x π) = f ( x). Weierstrass functions are nowhere differentiable yet continuous, and so is your f. A quote from wikipedia:

Weierstrass Function -- from Wolfram MathWorld

Web1 de abr. de 2009 · Using a few basics from integration theory, a short proof of nowhere-differentiability of Weierstrass functions is given. Restated in terms of the Fourier ... Duistermaat, J.J.: Self-similarity of “Riemann’s nondifferentiable function”. Nieuw Arch. Wiskd. (4) 9(3), 303–337 (1991) MATH MathSciNet Google Scholar ... Web1 de jan. de 2015 · On Weierstraß’ non-differentiable function Article Jan 1988 Compt Rendus Acad Sci Math Masayoshi Hata View Show abstract On the sum of a lacunary series Article Trans Moscow Math Soc A.S. Belov... detergent to make black clothes blacker

Pointwise analysis of Riemann

Web14 de mai. de 2009 · Abstract Nondifferential functions, Weierstrass functions, Vander Waerden type functions, and generalizations are considered in this chapter. In classical analysis, one of the problems that... WebThe function constructed is known as the Weierstrass }function. The second part of the theorem shows in some in some sense, }is the most basic elliptic function in that any other function can be written as a polynomial in }and its derivative. For the rest of this section, we x a lattice = h1;˝i. De nition 1.4. chunky cup handles