Define methods for airyai, airyaiprime, airybi, airybiprime

In Julia 0.6 Airy functions have been reorganized, see
JuliaLang/julia#18050.

I will keep a method for `airy' until support for Julia 0.5 will be
dropped.

src/math.jl

@@ -765,6 +765,7 @@ end
 lbeta(a::Real, b::Measurement) = lbeta(b, a)
 
 # Airy functions
+# TOOD: Remove method for `airy' when support for Julia 0.5 will be dropped.
 import Base: airy
 
 function airy(k::Integer, a::Measurement)
@@ -777,6 +778,23 @@ function airy(k::Integer, a::Measurement)
     end
 end
 
+import Base: airyai, airyaiprime, airybi, airybiprime
+
+for f in (:airyai, :airybi)
+    der = Symbol(string(f) * "prime")
+    @eval begin
+        function $f(a::Measurement)
+            x = a.val
+            return result($f(x), $der(x), a)
+        end
+        function $der(a::Measurement)
+            x = a.val
+            # Use Airy equation: y'' - xy = 0 => y'' = xy
+            return result($der(x), x * $f(x), a)
+        end
+    end
+end
+
 # Bessel functions
 import Base: besselj0, besselj1, besselj, bessely0, bessely1, bessely, besselh,
 besseli, besselix, besselk, besselkx

test/runtests.jl

@@ -325,10 +325,10 @@ for a in (x, y); test_approx_eq(lbeta(a, pi), log(beta(a, pi))); end
 for a in (x, y); test_approx_eq(lbeta(e, a), log(beta(e, a))); end
 
 # Airy functions
-test_approx_eq(airy(0, x), 0.006591139357460721 ± 0.0011912976705951322)
-test_approx_eq(airy(1, x), -0.01191297670595132 ± 0.0019773418072382165)
-test_approx_eq(airy(2, x), 14.037328963730136 ± 2.2922214966382017)
-test_approx_eq(airy(3, x), 22.922214966382015 ± 4.211198689119041)
+test_approx_eq(airyai(x), 0.006591139357460721 ± 0.0011912976705951322)
+test_approx_eq(airyaiprime(x), -0.01191297670595132 ± 0.0019773418072382165)
+test_approx_eq(airybi(x), 14.037328963730136 ± 2.2922214966382017)
+test_approx_eq(airybiprime(x), 22.922214966382015 ± 4.211198689119041)
 for a in (w, x, y); test_approx_eq(airy(a), airy(0, a)); end
 for a in (w, x, y); test_approx_eq(airyai(a), airy(0, a)); end
 for a in (w, x, y); test_approx_eq(airyprime(a), airy(1, a)); end