If we set out to prove the irrationality of the natural logarithm of π (pie), by writing out the Taylor series centered at zero for the function y=π^x, with x=1, we have:
π=1+Sum(ln^k(π)/k!) from k=1 to infinity.
Since we know π is irrational, then ln(π) must be irrational or otherwise...
Okay, let me clarify.
I wish to find a formula that will give me the nth derivative of the reciprocal of κ'[x].
Just as the the nth derivative of the function e^ax is given by a^n(e^ax); I'am looking for the equivalent with the above function. Whether the function for the nth derivative is...
Not Quite; just a function that when I enter, say n=1 , as its argument it results in it's first derivative and so on. I don't want to calculate the function at points or find a power/Taylor series representation.
I have tried to generalize but I can't find a pattern, using the quotient rule to...
Hi guys, I need help generalizing the derivative of the reciprocal of the function μ'(×).
What I would to find is a series representation whereby I don't have to find any derivatives of the function but merely replace powers and orders of derivatives.
Leibniz's series expression for the...