Problem 7. (20 points) We consider the function tanh(z) sinh(z) tanh(z)=cosh(z) where , For any integer...
Consider the following complex-variable function cosh a < T f(z) la! cosh πχ, a) Find all its singularities, state their nature and compute the residues b) Consider the rectangular contour y with vertices at tR and tRi. Evaluate 6 6 dz cosh πχ c) Using the previous result take the limit R-to prove that cosh ax (10] 2 cos (g Hint: remember that cosh(a + b) -cosh a cosh b + sinh a sinh b d) Why is the above...