This exercise illustrates a method of summing some infinite series. (a) Determine the residues at all the poles of the function
f(z)=πcotπza2+z2,f(z)=\frac{\pi \cot \pi z}{a^2+z^2}, f(z)=a2+z2πcotπz,
where aaa is a positive real constant. (b) By evaluating, in two different ways, the integral III of f(z)f(z)f(z) along the straight line joining −∞−ia/2-\infty-i a / 2−∞−ia/2 and +∞−ia/2+\infty-i a / 2+∞−ia/2, show that
∑n=1∞1a2+n2=πcothπa2a−12a2.\sum_{n=1}^{\infty} \frac{1}{a^2+n^2}=\frac{\pi \operatorname{coth} \pi a}{2 a}-\frac{1}{2 a^2} . n=1∑∞a2+n21=2aπcothπa−2a21.
(c) Deduce the value of ∑1∞n−2\sum_1^{\infty} n^{-2}∑1∞n−2.
C.Q. returns to the clinic two days later. The physician informs you that C.Q.'s Western blot test results confirm that she is HIV positive; he requests that you be present when he talks to her. Before leaving C.Q.'s room, the physician requests that you give C.Q. verbal and written information about local HIV support groups and help C.Q. cal l a friend to accompany her home this evening. She looks at you through her tears and states, "I can't believe it. J. is the only man I've had sex with since my divorce. He told me I had nothing to worry about. I can't believe he would do this to me.' C.Q. gives you the name and phone number of a relative she wants you to call. You remain with her until she leaves with her relative. Has C.Q.'s right to privacy been violated? Explain why or why not
Explain the difference between myopia and hyperopia.
Compare and contrast the function of phagocytes in the inflammatory response with the function of specific lymphocytes in the immune response.
