Editing Transcendental function (section)

==Examples==

The following functions are transcendental:

<math display="block">\begin{align}
f_1(x) &= x^\pi \\[2pt]
f_2(x) &= e^x \\[2pt]
f_3(x) &= \log_e{x} \\[2pt]
f_4(x) &= \cosh{x} \\
f_5(x) &= \sinh{x} \\
f_6(x) &= \tanh{x} \\
f_7(x) &= \sinh^{-1}{x} \\[2pt]
f_8(x) &= \tanh^{-1}{x} \\[2pt]
f_9(x) &= \cos{x} \\
f_{10}(x) &= \sin{x} \\
f_{11}(x) &= \tan{x} \\
f_{12}(x) &= \sin^{-1}{x} \\[2pt]
f_{13}(x) &= \tan^{-1}{x} \\[2pt]
f_{14}(x) &= x! \\
f_{15}(x) &= 1/x! \\[2pt]
f_{16}(x) &= x^x \\[2pt]
\end{align}</math>

For the first function <math>f_1(x)</math>, the exponent ''<math>\pi</math>'' can be replaced by any other irrational number, and the function will remain transcendental. For the second and third functions <math>f_2(x)</math> and <math>f_3(x)</math>, the base ''<math>e</math>'' can be replaced by any other positive real number base not equaling 1, and the functions will remain transcendental. Functions 4-8 denote the hyperbolic trigonometric functions, while functions 9-13 denote the circular trigonometric functions. The fourteenth function <math>f_{14}(x)</math> denotes the analytic extension of the factorial function via the [[gamma function]], and <math>f_{15}(x)</math> is its reciprocal, an entire function. Finally, in the last function <math>f_{16}(x)</math>, the exponent <math>x</math> can be replaced by <math>kx</math> for any nonzero real <math>k</math>, and the function will remain transcendental.