Advanced Search
All Posts : MaplePrimes Commons General Technical Discussions

MRB constant K part 2

Marvin Ray Burns 550 Maple
June 04 2010
0
This post in reply to the Post, MRB Constant K

 

If a function is differentiable at some point c of its domain, then it is also continuous at c. However here we extend the notion of differentiability to be valid for individual points on the real number line, specifically positive integers.

 f(n)=(-1)^n* n^(1/n)

THEOREM MRBK 8.0

f=f' / (I*Pi+(1-ln(n))/n^2)| n ∈ {1,2,3,...}

By THEOREM MRBK 4.0, When n is in the set of (positive) integers the derivative of f is exactly I*Pi*f+(1-ln(n))*f/n^2.

So f' = I*Pi*f+(1-ln(n))*f/n^2| n ∈ {1,2,3,...}

Solving for f, we have the following:

f' = I*Pi*f+(1-ln(n))*f/n^2

f' = f*(I*Pi+(1-ln(n))/n^2)

f=f' / (I*Pi+(1-ln(n))/n^2)

 

For more on this click here (W/A).
differentiation

Please Wait...