Mathematics

Show that, ignoring the singularity at the origin, the function given below is harmonic (partial Second differentiate u/ partial second differentiate x+Partial Second Differentiate u/ Partial Second Differentiate y=0 . u=ln(sqroot(x^2+y^2)).Show That, Ignoring The Singularity on the y axis ,the function given below is harmonic Partial Second Differentiate v/ Partial Second Differentiate X+Partial Second Differentiate v/ Partial Second Differentiate Y=0 . v=arctan(y/x)=a tan (y/x).Ignoring The Singularity show that the functions satistify the cauchy -riemann equations, partial differentiate u/partial Differentiate x=Partial Differentiate V/ Differentiate y, Partial Differentiate U/Partial Differentiate y=negative Partial Differentiate v/ Differentiate x.

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