diff --git a/include/pybind11/cast.h b/include/pybind11/cast.h
index 91c9ce753d..d10c989e64 100644
--- a/include/pybind11/cast.h
+++ b/include/pybind11/cast.h
@@ -15,6 +15,7 @@
 #include "detail/descr.h"
 #include "detail/internals.h"
 #include <array>
+#include <cmath>
 #include <limits>
 #include <tuple>
 #include <type_traits>
@@ -1871,6 +1872,18 @@ struct arg_v : arg {
     arg_v(const arg &base, T &&x, const char *descr = nullptr)
         : arg_v(arg(base), std::forward<T>(x), descr) { }
 
+#ifdef PYBIND11_CPP14
+#define ARGV_NAN_DEFAULT_OVERLOAD(FLOAT_TYPE) \
+    arg_v(const arg &base, FLOAT_TYPE x) \
+        : arg_v(arg(base), x, std::isnan(x) ? "numpy.nan" : nullptr) {}
+
+    ARGV_NAN_DEFAULT_OVERLOAD(float)
+    ARGV_NAN_DEFAULT_OVERLOAD(double)
+    ARGV_NAN_DEFAULT_OVERLOAD(long double)
+
+#undef ARGV_NAN_DEFAULT_OVERLOAD
+#endif
+
     /// Same as `arg::noconvert()`, but returns *this as arg_v&, not arg&
     arg_v &noconvert(bool flag = true) { arg::noconvert(flag); return *this; }
 
diff --git a/tests/test_kwargs_and_defaults.cpp b/tests/test_kwargs_and_defaults.cpp
index 8f095fe4a6..c17a0e08e0 100644
--- a/tests/test_kwargs_and_defaults.cpp
+++ b/tests/test_kwargs_and_defaults.cpp
@@ -13,6 +13,7 @@
 
 TEST_SUBMODULE(kwargs_and_defaults, m) {
     auto kw_func = [](int x, int y) { return "x=" + std::to_string(x) + ", y=" + std::to_string(y); };
+    auto kw_func_float = [](float x, double y, long double z) { return "x=" + std::to_string(x) + ", y=" + std::to_string(y) + ", y=" + std::to_string(z); };
 
     // test_named_arguments
     m.def("kw_func0", kw_func);
@@ -33,6 +34,14 @@ TEST_SUBMODULE(kwargs_and_defaults, m) {
     m.def("kw_func_udl", kw_func, "x"_a, "y"_a=300);
     m.def("kw_func_udl_z", kw_func, "x"_a, "y"_a=0);
 
+    m.def("kw_func_float_123", kw_func_float, "x"_a=1, "y"_a=2, "z"_a=3);
+#ifdef PYBIND11_CPP14
+    m.def("kw_func_float_nan", kw_func_float,
+        "x"_a=std::numeric_limits<float>::quiet_NaN(),
+        "y"_a=std::numeric_limits<double>::quiet_NaN(),
+        "z"_a=std::numeric_limits<long double>::quiet_NaN());
+#endif
+
     // test_args_and_kwargs
     m.def("args_function", [](py::args args) -> py::tuple {
         return std::move(args);
diff --git a/tests/test_kwargs_and_defaults.py b/tests/test_kwargs_and_defaults.py
index bad6636cb4..e61092eca2 100644
--- a/tests/test_kwargs_and_defaults.py
+++ b/tests/test_kwargs_and_defaults.py
@@ -10,6 +10,11 @@ def test_function_signatures(doc):
     assert doc(m.kw_func4) == "kw_func4(myList: List[int] = [13, 17]) -> str"
     assert doc(m.kw_func_udl) == "kw_func_udl(x: int, y: int = 300) -> str"
     assert doc(m.kw_func_udl_z) == "kw_func_udl_z(x: int, y: int = 0) -> str"
+    assert doc(m.kw_func_float_123) == "kw_func_float_123(x: float = 1, " \
+                                       "y: float = 2, z: float = 3) -> str"
+    if hasattr(m, "kw_func_float_nan"):
+        assert doc(m.kw_func_float_nan) == "kw_func_float_nan(x: float = numpy.nan, " \
+                                           "y: float = numpy.nan, z: float = numpy.nan) -> str"
     assert doc(m.args_function) == "args_function(*args) -> tuple"
     assert doc(m.args_kwargs_function) == "args_kwargs_function(*args, **kwargs) -> tuple"
     assert doc(m.KWClass.foo0) == \