Complex Analysis: Theory and Applications · Problem 5.1.17

Elementary Functions — Howell & Matthews

Mathematics — Complex Analysis · harmonic-functions

Problem

Use the fact that exp⁡(z2)\exp(z^2) is analytic to show that the function h(x,y)=ex2−y2sin⁡(2xy)h(x,y) = e^{x^2 - y^2}\sin(2xy) is harmonic.

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