Well I also come to think of it, disagree with calling the double factorial function the double factorial function, i would have thought bi-factorial to be better. or singular parity factorial function. 

But my interface (2016)  queries me everytime i enter "n!!" as to whether I am referring to the double factorial function or the application of the factorial twice in iteration, ie :  (n!)!

I just think this was a bad decision to make common place and the notation cabal need to review and change this. 

I really love this feature of course because it just allows you to learn so much about function properties via comparative learning processes, but I would also love to have the ability to:

1) Add elements to the list that is stored under known_functions:

FunctionAdvisor(known_functions);

2) Add my own categories of information such as the ones that exist like DE, branch_cuts, etc

I want to learn about why sometimes different algebraic expressions are ordered differently, and what would be the best way to instruct maple to chose a different "rule" for which a set of arithmetic functions are ordered, while still maintaining the axiom of uniqueness. 

I figured this would be accomplished on a case by case basis, and it may involve just using lists instead,defining a procedure to produce the desired ordering for any given set of functions, and using the "remove" command to replace the set "difference" operator and the Join command for the lists in place of the union operator. Then of course using the "Remove Duplicates" option from ListTools to impose the axiom of unique elements. 

Is this the best way to go about this, or is there a much simpler way, that includes an abstract algebra package that I'm unaware of thus far?

evalf[100](frac(exp(19*Pi)-19*Pi));

0.32853457802957784855876405976954586639886249604033514784046998713819112593

evalf[10](frac(exp(19*Pi)-19*Pi));

0.

Hello I don't mean this to the discredit of any others, and attempted to use the "contact user" feature, but the emails bounced, anyway I was hoping to get the user @Carl Love or @acer to assist me with this subject https://math.stackexchange.com/questions/2814343/finding-a-better-approximation-to-a-prime-number-relation

with(numtheory):

q := proc (h) options operator, arrow; min(`minus`(divisors(h*floor(ithprime(h)/h)), {1})) end proc;

DATA := [seq([h, simplify((h*igcd(h, h*q(h))-floor(sqrt(h))*igcd(floor(sqrt(h)), q(h)))^(1/2), 'radical')], h = 1 .. 300)];

plots[:-pointplot](DATA, color = "Black");