Maths for Engineers - 1

Problems On Dirichlet Integrals

Problems on Dirichlet Integrals:

 

Example1. First we note that with λ = 1 we recover the arc tangent formula

Similarly,

 

Example 2. For the Riemann zeta function

  

By contrast it is known as critical line.

More broadly,Crandall has shown that when 0 < σ < 1.

   

Now

 

Example3. These are the similar formulas for For instance applying for the result in the above with the sending functions

 

On using Euler result we get the above results.