Is the Weierstrass function even?

The Weierstrass ℘-function is an even elliptic function of order N=2 with a double pole at each lattice point and no other poles.

How do you write Weierstrass P?

Typography. The Weierstrass’s elliptic function is usually written with a rather special, lower case script letter ℘. In computing, the letter ℘ is available as \wp in TeX. In Unicode the code point is U+2118 ℘ SCRIPT CAPITAL P (HTML ℘ · ℘, &wp ), with the more correct alias weierstrass elliptic function.

What is Weierstrass model?

A Weierstrass equation or Weierstrass model over a field k is a plane curve E of the form y 2 + a 1 x y + a 3 y = x 3 + a 2 x 2 + a 4 x + a 6 , y^2 + a_1xy + a_3y = x^3 + a_2 x^2 + a_4 x + a_6, y2+a1xy+a3y=x3+a2x2+a4x+a6, with a 1 , a 2 , a 3 , a 4 , a 6 ∈ k a_1, a_2, a_3, a_4, a_6 \in k a1,a2,a3,a4,a6∈k.

What does ℘ mean?

noun mathematics Any of the Weierstrass elliptic functions .

What do you mean by Stone Weierstrass Theorem?

In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly approximated as closely as desired by a polynomial function. His result is known as the Stone–Weierstrass theorem.

What function Cannot be differentiated?

In the case of functions of one variable it is a function that does not have a finite derivative. For example, the function f(x)=|x| is not differentiable at x=0, though it is differentiable at that point from the left and from the right (i.e. it has finite left and right derivatives at that point).

Are differentiable functions dense in continuous functions?

The collection of continuous nowhere differentiable functions is dense in the Banach space X = C([0,1]) of continuous functions on [0,1] with the supremum norm.

Which is the inverse of the Weierstrass function?

The Weierstrass elliptic and related functions can be defined as inversions of elliptic integrals like and. Such integrals were investigated in the works of L. Euler (1761) and J.‐L. Lagrange (1769), who basically introduced the functions that are known today as the inverse Weierstrass functions.

Why is the Weierstrass derivative not an elliptic function?

Despite the commonly used naming convention, only the Weierstrass function and its derivative are elliptic functions because only these functions are doubly periodic. The other Weierstrass functions , , and are not elliptic functions because they are only quasi‐periodic functions with respect to .

Which is the solution of the Weierstrass differential equation?

The Weierstrass elliptic function arises as a solution to the following ordinary nonlinear differential equation:

Is the Weierstrass function math 104 proof of theorem?

The Weierstrass Function Math 104 Proof of Theorem. Since jancos(bnˇx)j an for all x2R and P 1 n=0 a n converges, the series converges uni-formly by the Weierstrass M-test. Moreover, since the partial sums are continuous (as nite sums of continuous functions), their uniform limit fis also continuous.