This is called tetration. Since the function does not have much use in most areas in mathematics, there is no standard way of notating this. The next natural step is pentation, which is repeated tetration; hexation, which is repeated pentation; heptation, which is repeated hexation; and so forth.

Since the up-arrow is used identically to the caret ( ^ ), tetration may be written as ( ^^ ); convenient for ASCII. has been around about as long. Allows for super-powers and super-exponential function by increasing the number of arrows; used in the article on large numbers.

Pentation can be written in array notation as /(/{a,b,3/}/), in chained arrow notation as /(a /rightarrow b /rightarrow 3/) and in Hyper-E notation as E(a)1#1#b. Pentation is less known than tetration, but there are a few googologisms employing it: 3 pentated to 3 is known as tritri, and 10 pentated to 100 is gaggol.

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Notation. Pentation is usually represented either by a triple up arrow: ↑↑↑ (Knuth, 1976) or by nx, where “x” is pentated to the nth power. 2 pentated to the nth power. Informally, it is sometimes represented as b^^^p.

Abstract. We consider the function called the power tower function, defined by iterated exponentiation of the real variable x. It is found to converge on the interval exp(−e)

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Definition of asymptote. : a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line.

The Green Neon Tetra is one of the most misidentified species in the tetra family. At first glance, it’s not hard to see why. They have the same shimmering blue stripe and plashes of red as their more famous cousins. However, the vividness of these colors is what distinguishes the Green Neon Tetra from other species. The red coloration is fainter.

Step 1: Look at the exponents in the denominator and numerator. If the largest exponent of the numerator is larger than… Step 2: The horizontal asymptote will be y = 0. That’s it! You’re done! Step 3: Enter your function into the y=editor. For example, you might have the function f (x) = (2x 2 –

The label() command used in the Asymptote code above is described in Section 4.4 of the Asymptote manual, with the following declaration: void label(picture pic=currentpicture, Label L, pair position, align align=NoAlign, pen p=currentpen, filltype filltype=NoFill) Janet //fnds this a bit overwhelming.