## How do you write Weierstrass P?

## 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 does ℘ mean?**

noun mathematics Any of the Weierstrass elliptic functions .

**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.

### 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.

**Can you integrate the Weierstrass function?**

The antiderivative of the Weierstrass function is fairly smooth, i.e. not too many sharp changes in slope. This just means that the Weierstrass function doesn’t rapidly change values (except in a few places). integrals, unlike derivatives, are highly insensitive to small changes in the function.

**Why is weierstrass function not differentiable?**

The higher-order terms create the smaller oscillations. With b carefully chosen as in the theorem, the graph becomes so jagged that there is no reasonable choice for a tangent line at any point; that is, the function is nowhere differentiable.

#### What is reverse A in maths?

Turned A (capital: Ɐ, lowercase: ɐ, math symbol ∀) is a letter and symbol based upon the letter A. The logical symbol ∀, has the same shape as a sans-serif capital turned A. It is used to represent universal quantification in predicate logic, where it is typically read as “for all”.

**What does heart struck mean?**

1 : struck to the heart. 2 archaic : driven to the heart : infixed in the mind.

**Is there a function with no derivative?**

In the case of functions of one variable it is a function that does not have a finite derivative. The continuous function f(x)=xsin(1/x) if x≠0 and f(0)=0 is not only non-differentiable at x=0, it has neither left nor right (and neither finite nor infinite) derivatives at that point.

## Can a continuous function be non differentiable?

In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable. For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.

**What functions are continuous but not differentiable?**

In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass.

**What is the name of upside down A?**

It was used in the 19th century by Charles Sanders Peirce as a logical symbol for ‘un-American’ (“unamerican”). The logical symbol ∀, has the same shape as a sans-serif capital turned A. It is used to represent universal quantification in predicate logic, where it is typically read as “for all”.

### What was the purpose of weierstrass’preparation theorem?

Weierstrass’ preparation theorem. A theorem obtained and originally formulated by K. Weierstrass in 1860 as a preparation lemma, used in the proofs of the existence and analytic nature of the implicit function of a complex variable defined by an equation f(z, w) = 0 whose left-hand side is a holomorphic function of two complex variables.

**Are there any rational functions in the Weierstrass function?**

so that all such functions are rational functions in the Weierstrass function and its derivative. One can wrap a single period parallelogram into a torus, or donut-shaped Riemann surface, and regard the elliptic functions associated to a given pair of periods to be functions defined on that Riemann surface.

**Is the Weierstrass theorem valid for trigonometric polynomials?**

The theorem is also valid for real-valued continuous 2π – periodic functions and trigonometric polynomials, e.g. for real-valued functions which are continuous on a bounded closed domain in an m – dimensional space, or for polynomials in m variables. For generalizations, see Stone–Weierstrass theorem.

#### How is the Weierstrass infinite product theorem generalized?

Weierstrass’ infinite product theorem can be generalized to the case of an arbitrary domain D ⊂ C : Whatever a sequence of points {αk} ⊂ D without limit points in D , there exists a holomorphic function f in D with zeros at the points αk and only at these points.