diff --git a/base/special/gamma.jl b/base/special/gamma.jl
index 5adc4d8d2aab5..d03185fc629e8 100644
--- a/base/special/gamma.jl
+++ b/base/special/gamma.jl
@@ -468,7 +468,9 @@ function polygamma(m::Integer, z::ComplexOrReal{Float64})
     # constants. We throw a DomainError() since the definition is unclear.
     real(m) < 0 && throw(DomainError())
 
-    s = m+1
+    s = Float64(m+1)
+    # It is safe to convert any integer (including `BigInt`) to a float here
+    # as underflow occurs before precision issues.
     if real(z) <= 0 # reflection formula
         (zeta(s, 1-z) + signflip(m, cotderiv(m,z))) * (-gamma(s))
     else
@@ -633,14 +635,14 @@ end
 
 for f in (:digamma, :trigamma, :zeta, :eta, :invdigamma)
     @eval begin
-		function $f(z::Union{ComplexOrReal{Float16}, ComplexOrReal{Float32}})
-			oftype(z, $f(f64(z)))
-		end
+        function $f(z::Union{ComplexOrReal{Float16}, ComplexOrReal{Float32}})
+            oftype(z, $f(f64(z)))
+        end
 
         function $f(z::Number)
             x = float(z)
             typeof(x) === typeof(z) && throw(MethodError($f, (z,)))
-            # There is nothing to fallback to, since this didn't change the argument types
+            # There is nothing to fallback to, as this didn't change the argument types
             $f(x)
         end
     end
@@ -650,15 +652,10 @@ end
 for T1 in (Float16, Float32, Float64), T2 in (Float16, Float32, Float64)
     (T1 == T2 == Float64) && continue # Avoid redefining base definition
 
-	@eval function zeta(s::ComplexOrReal{$T1}, z::ComplexOrReal{$T2})
-		ζ = zeta(f64(s), f64(z))
-
-		if typeof(s) <: Complex || typeof(z) <: Complex
-			convert(Complex{$T2}, ζ)
-		else
-			convert(typeof(z), ζ)
-		end
-	end
+    @eval function zeta(s::ComplexOrReal{$T1}, z::ComplexOrReal{$T2})
+        ζ = zeta(f64(s), f64(z))
+        convert(promote_type(typeof(s), typeof(z)),  ζ)
+    end
 end
 
 
@@ -672,13 +669,6 @@ function zeta(s::Number, z::Number)
     zeta(t, x)
 end
 
-# It is safe to convert `s` to a float as underflow will occur before precision issues
-zeta(s::Integer, z::Number) = zeta(oftype(z, s), z)
-function zeta(s::Integer, z::Integer)
-	x=float(z)
-	zeta(oftype(x, s), x)
-end
-
 
 function polygamma(m::Integer, z::Union{ComplexOrReal{Float16}, ComplexOrReal{Float32}})
     oftype(z, polygamma(m, f64(z)))
diff --git a/test/math.jl b/test/math.jl
index 15993027b8e33..9e4f8cee09921 100644
--- a/test/math.jl
+++ b/test/math.jl
@@ -960,13 +960,13 @@ end
 @test_throws MethodError zeta(1.0,big"2")
 @test_throws MethodError zeta(1.0,big"2.0")
 @test_throws MethodError zeta(big"1.0",2.0)
+@test_throws MethodError zeta(big"1",2.0)
 
 
-@test typeof(zeta(complex(1), 2.0)) == Complex{Float64}
 @test typeof(polygamma(3, 0x2)) == Float64
 @test typeof(polygamma(big"3", 2f0)) == Float32
-@test typeof(zeta(big"1", 2.0)) == Float64
-@test typeof(zeta(big"1", 2f0)) == Float32
-@test typeof(zeta(2f0, 2f0)) == Float32
+@test typeof(zeta(1, 2.0)) == Float64
+@test typeof(zeta(1, 2f0)) == Float64 # BitIntegers result in Float64 returns
 @test typeof(zeta(2f0, complex(2f0,0f0))) == Complex{Float32}
-@test typeof(zeta(complex(1,1), 2f0)) == Complex{Float32}
+@test typeof(zeta(complex(1,1), 2f0)) == Complex{Float64}
+@test typeof(zeta(complex(1), 2.0)) == Complex{Float64}