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On the Functional Equations f(x+iy)| = |f(x)+f(iy)| and |f(x+iy)| = |f(x)-f(iy)| and on Ivory's Theorem
Published online by Cambridge University Press: 20 November 2018
Extract
Considering Cauchy's functional equation
f(z1+z2)=f(z1)+ f(z2),
where f(z) is an entire function of z, we have the following functional equation:
(1) |f(x+iy)|=|f(x)+f(iy)|,
where x and y are real.
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- Copyright © Canadian Mathematical Society 1966
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