Merge pull request #439 from SciML/sf

using SpecialFunctions

Author: ChrisRackauckas

src/ModelingToolkit.jl

@@ -7,7 +7,7 @@ using MacroTools
 using UnPack: @unpack
 using DiffEqJump
 using DataStructures: OrderedDict, OrderedSet
-
+using SpecialFunctions, NaNMath
 using Base.Threads
 import MacroTools: splitdef, combinedef, postwalk, striplines
 import GeneralizedGenerated
@@ -122,7 +122,7 @@ export Differential, expand_derivatives, @derivatives
 export IntervalDomain, ProductDomain, ⊗, CircleDomain
 export Equation, ConstrainedEquation
 export Operation, Expression, Variable
-export independent_variable, states, parameters, equations 
+export independent_variable, states, parameters, equations
 
 export calculate_jacobian, generate_jacobian, generate_function
 export calculate_tgrad, generate_tgrad

src/differentials.jl

@@ -97,7 +97,7 @@ derivative(O::Operation, idx) = derivative(O.op, (O.args...,), Val(idx))
 derivative(O::Constant, ::Any) = Constant(0)
 
 # Pre-defined derivatives
-import DiffRules, SpecialFunctions, NaNMath
+import DiffRules
 for (modu, fun, arity) ∈ DiffRules.diffrules()
     fun in [:*, :+] && continue # special
     for i ∈ 1:arity

src/function_registration.jl

@@ -36,7 +36,7 @@ function typed_args(args)
 end
 
 # Binary & unary operators and functions
-import DiffRules, SpecialFunctions, NaNMath
+import DiffRules
 for (M, f, arity) in DiffRules.diffrules()
     fun = :($M.$f)
     sig = arity == 1 ? :($fun(x)) :