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Ex 9.5: Prove: if f(z) is analytic and real on a domain √2, then I is a constant function.

Ex 9.5: Prove: if f(z) is analytic and real on a domain √2, then I is a constant function.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Ex 9.5: Prove: if f(z) is analytic and real on a domain R then I is a constant function. Pf: I is analytic and real on √2 => f(x, y) = u(x, y) + i.0₂ namely √(x, y) =0; CR equations hold for every ZER I from analyticity on √}: OV 04 = 0 and -0 =0 OX by ду ди Du DX = By = 0 => M(x,y) = CEⓇR =) f(x,y) = c, namely & is a constant function. D -
Transcribed Image Text:Ex 9.5: Prove: if f(z) is analytic and real on a domain R then I is a constant function. Pf: I is analytic and real on √2 => f(x, y) = u(x, y) + i.0₂ namely √(x, y) =0; CR equations hold for every ZER I from analyticity on √}: OV 04 = 0 and -0 =0 OX by ду ди Du DX = By = 0 => M(x,y) = CEⓇR =) f(x,y) = c, namely & is a constant function. D -
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