# Find the standard factorization of the entire function f(z)=\cos \sqrt{z}

Find the standard factorization of the entire function $f\left(z\right)=\mathrm{cos}\sqrt{z}$
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Mason Hall
Step 1
To find standard factorization of entire function
$f\left(z\right)=\mathrm{cos}\sqrt{z}$
Step 2
Let z=x+iy
$f\left(z\right)=f\left(x+iy\right)=\mathrm{cos}\left(\sqrt{x+iy}\right)$
$\sqrt{x+iy}=\sqrt{{x}^{2}+{y}^{2}}$
$f\left(x+iy\right)=\mathrm{cos}\left(\sqrt{{x}^{2}+{y}^{2}}\right)$.

Archie Jones
Step 1
Using the Eulers