Merge pull request #66 from JuliaMath/oscardssmith-sinpi-tweak

improve accuracy of `besselk_power_series`

Author: heltonmc

src/besselk.jl

@@ -453,8 +453,7 @@ function besselk_power_series(v, x::ComplexOrReal{T}) where T
     # use the reflection identify to calculate gamma(-v)
     # use relation gamma(v)*v = gamma(v+1) to avoid two gamma calls
     gam_v = gamma(v)
-    xp1 = abs(v) + one(S)
-    gam_nv = π / (sinpi(xp1) * gam_v * v)
+    gam_nv = π / (sinpi(-abs(v)) * gam_v * v)
     gam_1mv = -gam_nv * v
     gam_1mnv = gam_v * v