Update README.md

Author: heltonmc

README.md

@@ -4,6 +4,80 @@ Implementations of Bessel's functions `besselj0`, `besselj1`, `bessely0`, `besse
 Most implementations are ported to Julia from the [Cephes](https://www.netlib.org/cephes/) math library  originally written by Stephen L. Moshier in the C programming language
 which are (partly) used in [SciPy](https://docs.scipy.org/doc/scipy/reference/special.html#faster-versions-of-common-bessel-functions) and [GCC libquadmath](https://gcc.gnu.org/onlinedocs/libquadmath/).
 
+# Quick start
+
+Only implemented for real arguments so far.
+
+```julia
+using Bessels
+
+# Bessel function of the first kind of order 0
+julia> besselj0(1.0)
+0.7651976865579665
+julia> besselj0(1.0f0)
+0.7651977f0
+
+# Bessel function of the first kind of order 1
+julia> besselj1(1.0)
+0.44005058574493355
+julia> besselj1(1.0f0)
+0.4400506f0
+
+# Bessel function of the second kind of order 0
+julia> bessely0(1.0)
+0.08825696421567697
+julia> bessely0(1.0f0)
+0.08825697f0
+
+# Bessel function of the second kind of order 1
+julia> bessely1(1.0)
+-0.7812128213002888
+julia> bessely1(1.0f0)
+-0.7812128f0
+
+# Modified Bessel function of the first kind of order 0
+julia> besseli0(1.0)
+1.2660658777520082
+julia> besseli0(1.0f0)
+1.266066f0
+
+# Scaled modified Bessel function of the first kind of order 0
+julia> besseli0x(1.0)
+0.46575960759364043
+julia> besseli0x(1.0f0)
+0.46575963f0
+
+# Scaled modified Bessel function of the first kind of order 1
+julia> besseli1x(1.0)
+0.2079104153497085
+julia> besseli1x(1.0f0)
+0.20791042f0
+
+# Modified Bessel function of the second kind of order 0
+julia> besselk0(1.0)
+0.42102443824070823
+julia> besselk0(1.0f0)
+0.42102447f0
+
+# Scaled modified Bessel function of the second kind of order 0
+julia> besselk0x(1.0)
+1.1444630798068947
+julia> besselk0x(1.0f0)
+1.1444632f0
+
+# Modified Bessel function of the second kind of order 1
+julia> besselk1(1.0)
+0.6019072301972346
+julia> besselk1(1.0f0)
+0.6019073f0
+
+# Scaled modified Bessel function of the second kind of order 1
+julia> besselk1x(1.0)
+1.636153486263258
+julia> besselk1x(1.0f0)
+1.6361537f0
+```
+
 # Benchmarks
 
 Comparing the relative speed (`SpecialFunctions.jl / Bessels.jl`) for a vector of values between 0 and 100.