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18.10. Let f be analytic inside and on the unit circle 7. Show that, for 0.

18.10. Let f be analytic inside and on the unit circle 7. Show that, for 0.

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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18.10. Let f be analytic inside and on the unit circle y. Show that, for 0<< 1, ƒ(E) ƒ(E) 2mif(z) = (²) de-1) d Hence, deduce the Poisson integral formula f(reio) = 2T - Sh 2T (1-²) 1-2r cos(0-t) +72 f (et)dt, 0<r<1.
Transcribed Image Text:18.10. Let f be analytic inside and on the unit circle y. Show that, for 0<< 1, ƒ(E) ƒ(E) 2mif(z) = (²) de-1) d Hence, deduce the Poisson integral formula f(reio) = 2T - Sh 2T (1-²) 1-2r cos(0-t) +72 f (et)dt, 0<r<1.
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