Cnder the transformation rr =exp::. the image of the
Chapter 0, Problem 9.30(choose chapter or problem)
Cnder the transformation rr =exp::. the image of the segment 0 ::: _r :::; ;r of they axis is the semicircle 11 2 + t 2 = I. t'::: 0 (SL"e Sec. 103). Also. the function ( 1 ) /1 h (11. t') = Re 2 - u + - = 2 - /1 + 0 . , IJ.' 11- + 1- is harmonic everywhere in the rr plane except for the origin: and it assumes the value h = 2 on the semicircle. Write an explicit expression for the function H(.r. y) in the theorem of Sec. 117. Then illustrate the theorem by showing directly that H = 2 along the segment 0 ~ y::: ;r of they axis.
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