This submission was more a challenge than a puzzle, though puzzling it may have been.
|_cosh(|_(cosh(]tan(0!)[)_|)_|! - 4 - 1 = 3628795
Under the requirements proposed, ideally the equation would be of the form F(x) = n, where F(x) was the combination of various math functions using the single smallest digit, i.e., 0 to seed the function and n equalling the largest number possible with the remaining digits, i.e., 987654321.
Using various math functions the result might possibly be attained. For instance, examine the following equation:
such that |_x_| is the floor function and ]x[ is the ceiling function.
As can be seen, with a single 0 a much larger number was acquired.
When I had submitted the challenge, I had limited myself to only a few functions. As such, the largest candidate I've found was:
p8# + 6$ * 1 = 9734250
- p8# (or 8#, the primorial of 8; 1st definition) = 9699690;
- 6$ (the superfactorial of 6) = 34560
As to the largest number for the digits 0 to 5, one candidate might be:(5!! - 4)# = 2310
- 5!! (the double factorial of 5) = 15;
- 11# (the primorial of 11; 2nd definition) = 2310