Complex Analysis: Theory and Applications · Problem 5.4.3

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · complex-trig-modulus

Problem

Show that Equation (5.40) simplifies to Equation (5.41). Hint: Use the facts that cosh⁡2y−sinh⁡2y=1\cosh^2 y - \sinh^2 y = 1 and sinh⁡2y=2cosh⁡ysinh⁡y\sinh 2y = 2\cosh y \sinh y.

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