31: ASIN(√4 / 4) + 4/4
32: 4 * √4 * √4 * √4
33: 4!! * 4 + 4/4 (see note below)
34: 44 - 4/.4
35: 4! + 44/4
36: 44 - 4 - 4
37: √4 baker's dozen + 44/4 ; ahem!!
38: 44 - 4 - √4
39: (√4 + √4 - 4/4) baker's dozen
40: 44 - √4 - √4
note below!
4!! = 8
https://en.wikipedia.org/wiki/Double_factorial
Double factorial could come in handy!! Must admit I've never heard of that.
I don't know about 31 (although pretty smart). Here's an alternative:
\(\displaystyle 31 = 4! + \frac {4! + 4}{4}\)
37 and 39 are dodgy, but not sure if these are any better:
37 = 44 - 4 - F
4 where F
4 =3 , the fourth Fibonacci number
39 = F
4 * F
4 * 4 + F
4
Moving on …
\(\displaystyle 41 = (4 + F
4)^{\sqrt4} - 4!!\) …. dodgy? (Edit: even LaTex doesn't like it)
\(\displaystyle 42 = 44 - 4 + \sqrt{4}\)
\(\displaystyle 43=44 - \frac{4}{4}\)
\(\displaystyle 44 = 44 + 4 - 4\)
\(\displaystyle 45 = 44 + \frac{4}{4}\)
\(\displaystyle 46 = 44 +4 - \sqrt{4}\)