From ee073698b5a0004128df7482bd74661de66672a4 Mon Sep 17 00:00:00 2001
From: Christoph Ruegg <git@cdrnet.ch>
Date: Fri, 21 Feb 2014 21:30:27 +0100
Subject: [PATCH] Docs: special functions, trigonometry

---
 docs/content/Functions.fsx | 34 +++++++++++++++++++++++++++++++---
 1 file changed, 31 insertions(+), 3 deletions(-)

diff --git a/docs/content/Functions.fsx b/docs/content/Functions.fsx
index 35f07f9a..f9ebd7d0 100644
--- a/docs/content/Functions.fsx
+++ b/docs/content/Functions.fsx
@@ -224,13 +224,20 @@ $$$
 Bessel and Struve Functions
 ---------------------------
 
-#### Modified Bessel functions
+#### Bessel functions
 
 Bessel functions are canonical solutions $y(x)$ of Bessel's differential equation
 
 $$$
 x^2\frac{\mathrm{d}^2y}{\mathrm{d}x^2}+x\frac{\mathrm{d}y}{\mathrm{d}x}+(x^2-\alpha^2)y = 0
 
+#### Modified Bessel functions
+
+Modified Bessel's equation:
+
+$$$
+x^2\frac{\mathrm{d}^2y}{\mathrm{d}x^2}+x\frac{\mathrm{d}y}{\mathrm{d}x}-(x^2+\alpha^2)y = 0
+
 Modified Bessel functions:
 
 $$$
@@ -281,14 +288,21 @@ Exponentially scaled modified Bessel function of the second kind, order 1.
 $$$
 x \mapsto e^x\mathrm{K}_1(x)
 
-
-#### Modified Struve functions
+#### Struve functions
 
 Struve functions are solutions $y(x)$ of the non-homogeneous Bessel's differential equation
 
 $$$
 x^2\frac{\mathrm{d}^2y}{\mathrm{d}x^2}+x\frac{\mathrm{d}y}{\mathrm{d}x}+(x^2-\alpha^2)y = \frac{4(\frac{x}{2})^{\alpha+1}}{\sqrt{\pi}\Gamma(\alpha+\frac{1}{2})}
 
+
+#### Modified Struve functions
+
+Modified equation:
+
+$$$
+x^2\frac{\mathrm{d}^2y}{\mathrm{d}x^2}+x\frac{\mathrm{d}y}{\mathrm{d}x}-(x^2+\alpha^2)y = \frac{4(\frac{x}{2})^{\alpha+1}}{\sqrt{\pi}\Gamma(\alpha+\frac{1}{2})}
+
 Modified Struve functions:
 
 $$$
@@ -343,4 +357,18 @@ x \mapsto e^x - 1
 $$$
 (a,b) \mapsto \sqrt{a^2 + b^2}
 
+
+Trigonometry
+------------
+
+The `Trig` class provides the complete set of fundamental trigonometric functions
+for both real and complex arguments.
+
+* **Trigonometric**: Sin, Cos, Tan, Cot, Sec, Csc
+* **Trigonometric Inverse**: Asin, Acos, Atan, Acot, Asec, Acsc
+* **Hyperbolic**: Sinh, Cosh, Tanh, Coth, Sech, Csch
+* **Hyperbolic Area**: Asinh, Acosh, Atanh, Acoth, Asech, Acsch
+* **Sinc**: Normalized sinc function $x \mapsto \frac{\sin\pi x}{\pi x}$
+* Conversion routines between radian, degree and grad.
+
 *)