I consider a smooth function f over the real numbers, the derivatives are f(k). I suppose that:
0<f(n+1)(x)≤f(n)(x)
for all n∈N and all x∈R. Then I suppose that for x≅−∞, f(x)∼ex, (f is equivalent to ex in −∞); have we in these conditions:
f(x)=ex
This problem may have a meaning in physics because if t is the time, x=ln(t), we have near the Big Bang t=0, x≅−∞, so that f is in fact the time.