5. Let u be harmonic on the complex plane. Show that for any complex number a and r > 0, u(a) = 2²/7 ²* u(a + re¹0) do. 2π (This is the 'Mean value Theorem' for harmonic functions.) Conclude that |u(a)| ≤max_u(a + rei). 0≤0<2T
5. Let u be harmonic on the complex plane. Show that for any complex number a and r > 0, u(a) = 2²/7 ²* u(a + re¹0) do. 2π (This is the 'Mean value Theorem' for harmonic functions.) Conclude that |u(a)| ≤max_u(a + rei). 0≤0<2T
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 35E
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This is for a course in complex analysis. The main topics we have covered in this section are power series expansions and Cauchy's Formula. We have NOT covered residues. We must end with the part involving the inequality at the bottom.
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