diff --git a/test/Li.jl b/test/Li.jl
index 7217d8d..7ae32e1 100644
--- a/test/Li.jl
+++ b/test/Li.jl
@@ -63,17 +63,20 @@ end
         @test PolyLog.li(n, Float16(1.0)) ≈ zeta
         @test PolyLog.li(n, 1//1) ≈ zeta
         @test PolyLog.li(n, 1) ≈ zeta
+        @test PolyLog.li(n, BigFloat("1.0")) == PolyLog.zeta(n, BigFloat)
 
         @test PolyLog.li(n, 1.0 + 0.0im) == zeta
         @test PolyLog.li(n, 1.0f0 + 0.0f0im) ≈ zeta
         @test PolyLog.li(n, ComplexF16(1.0 + 0.0im)) ≈ zeta
         @test PolyLog.li(n, 1//1 + 0//1im) ≈ zeta
         @test PolyLog.li(n, 1 + 0im) ≈ zeta
+        @test PolyLog.li(n, BigFloat("1.0") + 0im) == PolyLog.zeta(n, BigFloat)
     end
 
     # value close to boundary between series 1 and 2 in arXiv:2010.09860
-    @test PolyLog.li(-2, -0.50001)   ≈ -0.074072592582716422 atol=1e-14
-    @test PolyLog.reli(-2, -0.50001) ≈ -0.074072592582716422 atol=1e-14
+    @test PolyLog.li(-2, -0.50001)               ≈ -0.074072592582716422 atol=1e-14
+    @test PolyLog.reli(-2, -0.50001)             ≈ -0.074072592582716422 atol=1e-14
+    @test PolyLog.li(-2, BigFloat("-0.50001"))   ≈ -0.074072592582716422 atol=1e-14
     @test PolyLog.reli(-2, BigFloat("-0.50001")) ≈ -0.074072592582716422 atol=1e-14
 
     # value sensitive to proper treatment of 0.0 vs -0.0 in imag(z)
@@ -86,12 +89,15 @@ end
     @test isinf(PolyLog.reli(10, Inf))
     @test isinf(PolyLog.reli(10, BigFloat(Inf)))
     @test isnan(PolyLog.li(10, NaN))
+    @test isnan(PolyLog.li(10, BigFloat(NaN)))
     @test isinf(PolyLog.li(10, Inf))
+    @test isinf(PolyLog.li(10, BigFloat(Inf)))
 
     # test type stability
     for T in (Float16, Float32, Float64, BigFloat)
         for n in -10:10
             for x in (NaN, Inf, -2, -1, 0, 1, 2, 3)
+                @test typeof(PolyLog.li(n, convert(Complex{T}, x))) == Complex{T}
                 @test typeof(PolyLog.reli(n, convert(T, x))) == T
             end
         end