Mathematical Methods in the Physical Sciences · Problem 11.13

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · residues-at-given-points

Problem

Find the residues at the given points. (a)

\dfrac{\cos z}{(2z-\pi)^4}

\dfrac{\pi}{2}

(b)

\dfrac{2z^2+3z}{z-1}

\infty

(c)

\dfrac{z^3}{1+32z^5}

z = -\tfrac{1}{2}

(d)

\csc(2z-3)

z = \tfrac{3}{2}