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I've got a problem I'm working out with some program I'm writing that requires knowing as many direct functions of a number as possible.

I know I'm messing technical terminology up extremely badly, but allow me to explain myself:

If I have a number n, I want to know as many functions as possible that are commonly recognized like this:

cos(n)

n!

tanh(n)

sqrt(n)

and so on.

I don't want functions that would use numbers, though.

The fourth root of n would be invalid because it uses 4.

Log base e of n would be invalid because it uses e, however ln(n) is acceptable because it isn't written with the number e.

I know it's a very vague question, but as a Pre-Calc student I am sure there's many I haven't been exposed to.

Thanks for any help!

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    The question doesn't make sense IMO. You say the square root is a "direct function" and the fourth root is not but the square root is related to $2$ the same way that the fourth root is related to $4$. By the way, though it's less obvious, the other functions in your list "use numbers" too. I don't think it's possible to come up with any reasonable definition of what a "direct function" is. – 2017-02-25
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    So what you really want has nothing to do with functions, rather the popular notation used for various functions? What's your threshold for "commonly recognized"? Most pre-calc students wouldn't recognize tanh. – 2017-02-25
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    @mathematician Good question... I meant commonly recognized as if I sent a mathematician whateverFunction(_n_), they would understand what the output would be. Something like cos(n) is commonly recognized. – 2017-02-25
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    @Qudit I used "direct function" because I didn't really know the word for it. I am completely aware that other functions in my list "use numbers" too. I'm working out a "fun mathematical challenge," and while most of these things will use numbers, I'm looking for the ones which imply them rather than write them. ln(_n_) is implied while log base e of _n_ is explicit. – 2017-02-25

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Depends on what counts as "commonly recognized". All the trig and hyperbolic trig functions, and their inverses ($\arcsin x$, and so on). cbrt(x) is recognized (by some people!) as the cube root. $\log x$ is the natural logarithm of $x$, and $\exp(x)$ is recognized for $e^x$. Then there are the Jacobi elliptic functions sn, cn, and dn. And the Lambert function $W(x)$. And the Gamma function $\Gamma(z)$. And the Riemann zeta-function $\zeta(s)$. And $\pi(x)$, the prime-counting function. And many, many more.

You may find https://en.wikipedia.org/wiki/List_of_mathematical_functions useful.

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    Also https://en.wikipedia.org/wiki/List_of_mathematical_abbreviations – 2017-02-25