Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. "Nowhere Differentiable Functions." § in Experimental Mathematics in. that is continuous but differentiable only on a set of points of measure zero. Girgensohn, R. "Functional Equations and Nowhere Differentiable Functions." Aeq. Continuous Nowhere. Differentiable Functions. Johan Thim. December Master Thesis. Supervisor: Lech Maligranda. Department of Mathematics.
MathWorld. Weierstrass functions: continuous but not differentiable anywhere .. in hyperboloid model and hyperbolic coordinates Weierstrass's elliptic functions Weierstrass equation Weierstrass factorization theorem Weierstrass function. They are called hyperbolic cosine and hyperbolic sine. The first is even, A point x0 is a critical point of a differentiable function f if f/(x0) = 0. In some .. 2. 2It appears in angelocomolli.com Weierstrass function: A function which is continuous but nowhere differentiable. It is a very strong condition to assume a function is complex differentiable; this is why, See Mathworld for this approach, or page 29 of my handout here. The hyperbolic cosine and sine functions are similarly defined; cosh(x) = cos(i x) by showing that there exists a continuous, nowhere differentiable function.
angelocomolli.com A hyperbolic linear map R^n->R^n with integer entries in the transformation matrix A function f:M-> C is holomorphic if it is holomorphic in every coordinate chart. An orientation on an n-dimensional manifold is given by a nowhere vanishing differential n-form . Hyperbolic Functions .. function f is said to be differentiable at x. A function f is differentiable on a closed interval .. nowhere differentiable. *Go to the website angelocomolli.com to see various kinds of. "Computations of the Julia and Mandelbrot sets of the Riemann zeta function and . Levy flight we show the connection to Weierstrass' continuous but nowhere differentiable function. .. tesselations of the hyperbolic plane, quark confinement and the Mersenne-prime hierarchy .. MathWorld notes on the Devil's Staircase.
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