Mathematical Methods in the Physical Sciences · Problem 11.14

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · residues-at-given-points

Problem

Find the residues at the given points. (a) ln⁡(1+2z)z2\dfrac{\ln(1+2z)}{z^2} at 00 (b) 1zsin⁡(2z+5)\dfrac{1}{z}\sin(2z+5) at ∞\infty (c) z34z4+1\dfrac{z^3}{4z^4+1} at 12(1+i)\tfrac{1}{2}(1+i) (d) zsin⁡2z(z+π)2\dfrac{z\sin 2z}{(z+\pi)^2} at −π-\pi

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