I just want some quick clarification on some notation. If we have a variable defined by a function, such as: $$Z=f(E)$$ then we know both of these are different notations for the derivative: $$\frac{dZ}{dE}=f'(E)$$ If instead I see this notation $$\frac{d(Z/E)}{dE}$$ and I let $$g(E)=f(E)/E$$ doe...
For any positive integer $n$ the left factorial function is defined as $$!n = 0!+1!+2!+\cdots+(n-1)!$$ My work: Consider a $p$-dimensional Euclidean space with orthogonal coordinates, and take the two vectors $$ X = [ 0!, 1!, 2!,\cdots, (p-1)! ]$$ $$Y = [ (p-1)!,\cdots, 2!, 1!, 0! ]$$ The dot p...
I had recently asked this question which shortly after posting got three downvotes. I can't seem to understand why. I suspect that it has something to do with the level of how speculative it is. However I think it was somewhat unjust. To be more elaborate, the reason I thought that the question g...
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