Approximating a simple sum Can somone help me find

Jerimiah Hansen

Jerimiah Hansen

Answered question

2022-03-15

Approximating a simple sum
Can somone help me find an assymptotic formula for n, for fixed x , for this sum , perhaps an inequality would be even better, or some bound on the error.
k=1n1log(kx)
I need somthing better then the integral from 1 to n of ln(kx) with respect to k. Its also okay if you use special functions, like the logarithmic integral.

Answer & Explanation

bridgedcuu

bridgedcuu

Beginner2022-03-16Added 7 answers

The Euler-Maclaurin series for k1log(kx) starts
F(k)=Li(kx)x-12ln(kx)-112ln(kx)2k+3+3ln(kx)+ln(kx)2360ln(kx)4k3+
That is, we should have
k=1n1log(kx)F(n+1)+C
where C is a constant.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?