Notation question (1 Viewer)

[leehuan]

WolframAlpha uses it, but I never see it anywhere else. So is this technically incorrect notation?

 

[Paradoxica]

WolframAlpha uses it, but I never see it anywhere else. So is this technically incorrect notation?

No, it is the international standard for raising logarithmic functions to arbitrary powers. Most number theory papers, that I've seen, that have exponentiated logarithms, use it.

Iterated Logarithms are a different matter entirely.

 

[KingOfActing]

It depends on the context you're working in. Sometimes it's useful for , other times for . Neither is more correct than the other. Additionally, usually represents the inverse function, rather than the reciprocal of the function. usually represents the nth derivative when n is positive, and the nth primitive when n is negative, and the function itself when n is 0.

 

[leehuan]

No, it is the international standard for raising logarithmic functions to arbitrary powers. Most number theory papers, that I've seen, that have exponentiated logarithms, use it.

Iterated Logarithms are a different matter entirely.

Have no clue why I've never come across this anymore.

And yes, that I am aware of. That's the same with saying sin(sin(x))

It depends on the context you're working in. Sometimes it's useful for , other times for . Neither is more correct than the other. Additionally, usually represents the inverse function, rather than the reciprocal of the function. usually represents the nth derivative when n is positive, and the nth primitive when n is negative, and the function itself when n is 0.

Pretty sure the function of a function notation was something along the lines of f bullet f(x).

Yes, f^-1(x) I'm aware of of course and f^'bracketed-index'(x) is an nth derivative

But even then inverse sine can be written using the arcsin(x) notation

 

[KingOfActing]

I should say that the majority of the time I see it means the nth iterate of the function, except in the case of the trigonometric functions. https://en.wikipedia.org/wiki/Iterated_function

 

[InteGrand]

 

[braintic]

In Linear Algebra, matrix multiplication is equivalent to function composition.

If a matrix M represents a function f, then M^2 represents f^2, but M^2 is a multiplication and f^2 is a composition.

The composition power notation is regular used in Linear Algebra, but only on generic function f, not on specific functions such as log.