Show that the given function is not analytic at any point. (Assume z = x + ¡y.) f(z) = x² + y² UE av 0x The Cauchy-Riemann equations hold only at (x, y) = S 11 du ax av ду อน ay FI BE HE Since there
Show that the given function is not analytic at any point. (Assume z = x + ¡y.) f(z) = x² + y² UE av 0x The Cauchy-Riemann equations hold only at (x, y) = S 11 du ax av ду อน ay FI BE HE Since there
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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![in equations hold only at (x, y) = [
Since there is no neighborhood about this point within which fis differentiable we conclude f Is nowhere analytic.
k](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F283a229b-00a6-4962-bdd6-fa2744e9b2f7%2Fafa904c0-37d3-479b-88a6-202333010e0d%2Fxp4sh0j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:in equations hold only at (x, y) = [
Since there is no neighborhood about this point within which fis differentiable we conclude f Is nowhere analytic.
k
![Show that the given function is not analytic at any point. (Assume z = x + ¡y.)
f(z) = x² + y²
UE
av
0x
The Cauchy-Riemann equations hold only at (x, y) =
S
11
du
ax
av
dy
au
ду
BI
BE
HE
Since there](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F283a229b-00a6-4962-bdd6-fa2744e9b2f7%2Fafa904c0-37d3-479b-88a6-202333010e0d%2Fyp9leum_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show that the given function is not analytic at any point. (Assume z = x + ¡y.)
f(z) = x² + y²
UE
av
0x
The Cauchy-Riemann equations hold only at (x, y) =
S
11
du
ax
av
dy
au
ду
BI
BE
HE
Since there
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