diff --git a/Project.toml b/Project.toml
index 9ad97054c..08e12b6ff 100644
--- a/Project.toml
+++ b/Project.toml
@@ -9,21 +9,22 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+ZygoteRules = "700de1a5-db45-46bc-99cf-38207098b444"
 
 [compat]
 Compat = "2.2"
 Distances = "0.8"
 PDMats = "0.9"
-SpecialFunctions = "0"
+SpecialFunctions = "0.8, 0.9"
 StatsFuns = "0.8"
-Zygote = "0.4"
+ZygoteRules = "0.2"
 julia = "1.0"
 
 [extras]
+FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Random", "Test", "FiniteDifferences"]
+test = ["Random", "Test", "FiniteDifferences", "Zygote"]
diff --git a/src/KernelFunctions.jl b/src/KernelFunctions.jl
index d6f18dcd0..847c27d33 100644
--- a/src/KernelFunctions.jl
+++ b/src/KernelFunctions.jl
@@ -16,8 +16,8 @@ export Transform, SelectTransform, ChainTransform, ScaleTransform, LowRankTransf
 
 using Compat
 using Distances, LinearAlgebra
-using SpecialFunctions: lgamma, besselk
-using Zygote: @adjoint
+using SpecialFunctions: logabsgamma, besselk
+using ZygoteRules: @adjoint
 using StatsFuns: logtwo
 using PDMats: PDMat
 
diff --git a/src/kernels/matern.jl b/src/kernels/matern.jl
index 63b856c91..8d41f4edb 100644
--- a/src/kernels/matern.jl
+++ b/src/kernels/matern.jl
@@ -33,7 +33,7 @@ end
 params(k::MaternKernel) = (params(transform(k)),k.ν)
 opt_params(k::MaternKernel) = (opt_params(transform(k)),k.ν)
 
-@inline kappa(κ::MaternKernel, d::Real) = iszero(d) ? one(d) : exp((1.0-κ.ν)*logtwo-lgamma(κ.ν) + κ.ν*log(sqrt(2κ.ν)*d)+log(besselk(κ.ν,sqrt(2κ.ν)*d)))
+@inline kappa(κ::MaternKernel, d::Real) = iszero(d) ? one(d) : exp((1.0-κ.ν)*logtwo-logabsgamma(κ.ν)[1] + κ.ν*log(sqrt(2κ.ν)*d)+log(besselk(κ.ν,sqrt(2κ.ν)*d)))
 
 """
 `Matern32Kernel([ρ=1.0])`