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

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Chapter2: Second-order Linear Odes
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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
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
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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