The Hedera Function is a complex semi-notation format of Hyperfactorial Array Notation.

The Hedera function comes from obscure symbols, also known as a fleuron, the hedera being this: ❦ (By the way, you can obtain this by using unicode U+2766)

Here is the Hedera function: ❦(x)= (x!^(((x!^(x!-1)!^…(1)!)((x!-1)!^…)!)((x!-2)!)… … ^ (x-1)!…^^(x-2)!^^^…[x-tration] 1!)) ! ! !

Alternatively, you could say x!^ H(H(H(x!)!)!)!!)!!!

Update #1: I've rewritten the function to better fit the functionality (no pun intended) of the ❦ function, as well as secondary and tertiary formulae, which is essentially this: If you use the ❦(x), the function is ___; If you use ❦(❦(x)) then it's the hedera function of the hedera function of x, but if you use ❦❦(x), then the function is different than the hedera funct of hedera funct of x.

Original ❦ function revised: Now the hedera function was an extremely fast-growing function as it is. The Original ❦ function was actually this:

(X!^((x!^x!-1^x!-2^x!-3^...3!^2!^1!)*(x!-1^x!-2^x!-3^x!-4^...2!^1!)*...2!^1!*1!))!

To reiterate this, this is a form of hyperfactorial, where this is x! to the power x! up ( up=to the power of) (x!-1)up (x!-2) up (x!-3) repeating until it gets to ^1. Then that is multiplied up to the point of the first exponent with the same thing as earlier, but starting at (x!-1), then (x!-2) multiplying until it is multiplied by one. After all of that, it is finally ended with one final factorial. So all of the previous work done is ended with a factorial. Excessive factorials, but it's a function of factorials.

Update #2: As I previous stated, I was coming up with ways of using the same symbol meaning different things. I have 2 more uses for the hedera function. The first usage is the secondary ❦ function, using this as a different symbol,this being U+2767, the bullet form of the hedera, ❧. This format of the hedera function, but instead this is a pyramidal hedera function, so instead of just doing multiplication on the 1st exponent "base," it multiplies on every exponential level.

Update #3: The third and final update is the fastest growing hedera function, and possibly fastest-growing function as of 10/29/14, I personally can't do the comparative function rate system...yet. This new function, which is a combo of the both hedera symbols is this: The tertiary hedera function is the same as the secondary, but replace all factorials for superfactorial factorial, so (x superfactorial) factorial, in that manner. Also at the end, using HAN, add a ? Symbol denoting the same as the BIGG, being this: H(x!)[<1-x!>(x!)]1 Tachyonic Encrypter