export bessely

Author: heltonmc

src/Bessels.jl

@@ -7,6 +7,7 @@ export besselj1
 
 export bessely0
 export bessely1
+export bessely
 
 export besseli
 export besselix

src/bessely.jl

@@ -187,7 +187,7 @@ end
 Bessel function of the first kind of order nu, ``J_{nu}(x)``.
 Nu must be real.
 """
-function _bessely(nu, x::T) where T
+function bessely(nu, x::T) where T
 
     # use forward recurrence if nu is an integer up until it becomes inefficient
     (isinteger(nu) && nu < 250) && return besselj_up_recurrence(x, bessely1(x), bessely0(x), 1, nu)[1]

test/bessely_test.jl

@@ -74,7 +74,7 @@ nu = [0, 1, 2, 4, 6, 10, 15, 20, 25, 30, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85,
 for v in nu, xx in x
     xx *= v
     sf = SpecialFunctions.bessely(BigFloat(v), BigFloat(xx))
-    @test isapprox(Bessels._bessely(v, xx), Float64(sf), rtol=2e-13)
+    @test isapprox(bessely(v, xx), Float64(sf), rtol=2e-13)
 end
 
 # test decimal orders
@@ -84,5 +84,5 @@ x = [0.05, 0.1, 0.2, 0.25, 0.3, 0.4, 0.5,0.55,  0.6,0.65,  0.7, 0.75, 0.8, 0.85,
 nu = [0.1, 0.4567, 0.8123, 1.5, 2.5, 4.1234, 6.8, 12.3, 18.9, 28.2345, 38.1235, 51.23, 72.23435, 80.5, 98.5, 104.2]
 for v in nu, xx in x
     xx *= v
-    @test isapprox(Bessels._bessely(v, xx), SpecialFunctions.bessely(v, xx), rtol=5e-12)
+    @test isapprox(bessely(v, xx), SpecialFunctions.bessely(v, xx), rtol=5e-12)
 end