Editing Entire function (section)

===Examples===
Here are some examples of functions of various orders:

====Order ''ρ''====
For arbitrary positive numbers <math>\rho</math> and <math>\sigma</math> one can construct an example of an entire function of order <math>\rho</math> and type <math>\sigma</math> using:

<math display="block">f(z)=\sum_{n=1}^\infty \left (\frac{e\rho\sigma}{n} \right )^{\frac{n}{\rho}} z^n</math>

====Order 0====
* Non-zero polynomials
*<math>\sum_{n=0}^\infty 2^{-n^2} z^n</math>

====Order 1/4====
<math display="block">f(\sqrt[4]z)</math> 
where <math display="block">f(u)=\cos(u)+\cosh(u)</math>

====Order 1/3====
<math display="block">f(\sqrt[3]z)</math>
where
<math display="block">f(u)=e^u+e^{\omega u}+e^{\omega^2 u} = e^u+2e^{-\frac{u}{2}}\cos \left (\frac{\sqrt 3u}{2} \right ), \quad \text{with } \omega \text{ a complex cube root of 1}.</math>

====Order 1/2====
<math display="block">\cos \left (a\sqrt z \right )</math> with <math>a\neq 0</math> (for which the type is given by <math>\sigma=|a|</math>)

====Order 1====
*<math>\exp(az)</math> with <math>a\neq 0</math> (<math>\sigma=|a|</math>)
*<math>\sin(z)</math>
*<math>\cosh(z)</math>
*the [[Bessel function]]s <math>J_n(z)</math> and spherical Bessel functions <math>j_n(z)</math> for integer values of <math>n</math><ref>See asymptotic expansion in Abramowitz and Stegun, [https://personal.math.ubc.ca/~cbm/aands/page_377.htm p. 377, 9.7.1].</ref>
*the [[reciprocal gamma function]] <math>1/\Gamma(z)</math> (<math>\sigma</math> is infinite)
*<math>\sum_{n=2}^\infty \frac{z^n}{(n\ln n)^n}. \quad (\sigma=0)</math>

====Order 3/2====
* [[Airy function]] <math>Ai(z)</math>

====Order 2====
*<math>\exp(az^2)</math> with <math>a\neq 0</math> (<math>\sigma=|a|</math>)
*The [[Barnes G-function]] (<math>\sigma</math> is infinite).

====Order infinity====
*<math>\exp(\exp(z))</math>