I was reading through my Calculus Textbook. When I got the chapter on transcendental functions it mentioned how to integrate and differentiate them. The only functions it mentioned were exponential, logarithmic, and trigonometric functions ex{$e^x$,$\log(x)$, and $\sin(x)$}
My question is there other types of transcendental functions, and if so what are they?
Transcental functions are all those functions which are not algebraic. There is no way of decribing them all. One example is the gamma function:$$\Gamma(t)=\int_0^{+\infty}e^{-x}x^{t-1}\,\mathrm dx.$$Another example is Riemann's zeta function$$\zeta(s)=\sum_{n=1}^\infty\frac1{n^s}.$$But there are lots and lots of other examples. Simpler ones are the hyperbolic sine and the hyperbolic cosine:$$\sinh(x)=\frac{e^x-e^{-x}}2\text{ and }\cosh(x)=\frac{e^x+e^{-x}}2.$$