# landau

1. ### Intuitive order of definitions in arithmetic

I have recently read through much of Edmund Landau's Foundations of Analysis but have wondered if there is a more intuitive order of defining fractions, division, negatives, subtraction, etc. Is there a book, website or even a video series anyone can recommend that presents such an order and...
2. ### Landau inequality

Let f 2 times differentiable function in open interval (-r,r), when r>0. There are two numbers M,N>0 so that |f ''(x)|<=N , |f(x)|<=M for all x in (-r,r). Prove that |f ' (0) | <= 2sqrt(M*N) + 2*M/r
3. ### Limit (~ is Landau's symbol in this Qs)

Hi everyone: I got a question which is about limit, after thinking still don't know how to starts it. please help!!!! Q:prove that (n+a)!/(n+b)! ~ n^(a-b) as n goes to +ive infinite (for fixed a,b>0) and the Qs provide some formula to use Euler's limit...
4. ### Maclaurin series and Landau's big "Oh" problem.

I have found the first 5 Taylor polynomials about x=0 for cosh(x). Being p0=1, p1=1, p2=1+\frac{1}{2}x^2, p3=1+\frac{1}{2}x^2, p4=1+\frac{1}{2}x^2+\frac{1}{24}x^4. How do I Find the Maclaurin series for cosh(x)? I can see it should be something like f(x) \approx \sum_{n = 1}\frac{x^{2n}}{2n!}...