diff --git a/stdlib/functools.pyi b/stdlib/functools.pyi
index 27550cfe08e6..42df655df67e 100644
--- a/stdlib/functools.pyi
+++ b/stdlib/functools.pyi
@@ -30,6 +30,7 @@ if sys.version_info >= (3, 9):
 _T = TypeVar("_T")
 _T_co = TypeVar("_T_co", covariant=True)
 _S = TypeVar("_S")
+_P = ParamSpec("_P")
 _PWrapped = ParamSpec("_PWrapped")
 _RWrapped = TypeVar("_RWrapped")
 _PWrapper = ParamSpec("_PWrapper")
@@ -52,21 +53,21 @@ if sys.version_info >= (3, 9):
         typed: bool
 
 @final
-class _lru_cache_wrapper(Generic[_T]):
-    __wrapped__: Callable[..., _T]
-    def __call__(self, *args: Hashable, **kwargs: Hashable) -> _T: ...
+class _lru_cache_wrapper(Generic[_P, _T]):
+    __wrapped__: Callable[_P, _T]
+    def __call__(self, *args: _P.args, **kwargs: _P.kwargs) -> _T: ...
     def cache_info(self) -> _CacheInfo: ...
     def cache_clear(self) -> None: ...
     if sys.version_info >= (3, 9):
         def cache_parameters(self) -> _CacheParameters: ...
 
-    def __copy__(self) -> _lru_cache_wrapper[_T]: ...
-    def __deepcopy__(self, memo: Any, /) -> _lru_cache_wrapper[_T]: ...
+    def __copy__(self) -> Self: ...
+    def __deepcopy__(self, memo: Any, /) -> Self: ...
 
 @overload
-def lru_cache(maxsize: int | None = 128, typed: bool = False) -> Callable[[Callable[..., _T]], _lru_cache_wrapper[_T]]: ...
+def lru_cache(maxsize: int | None = 128, typed: bool = False) -> Callable[[Callable[_P, _T]], _lru_cache_wrapper[_P, _T]]: ...
 @overload
-def lru_cache(maxsize: Callable[..., _T], typed: bool = False) -> _lru_cache_wrapper[_T]: ...
+def lru_cache(maxsize: Callable[_P, _T], typed: bool = False) -> _lru_cache_wrapper[_P, _T]: ...
 
 if sys.version_info >= (3, 12):
     WRAPPER_ASSIGNMENTS: tuple[
@@ -199,7 +200,7 @@ class cached_property(Generic[_T_co]):
         def __class_getitem__(cls, item: Any) -> GenericAlias: ...
 
 if sys.version_info >= (3, 9):
-    def cache(user_function: Callable[..., _T], /) -> _lru_cache_wrapper[_T]: ...
+    def cache(user_function: Callable[_P, _T], /) -> _lru_cache_wrapper[_P, _T]: ...
 
 def _make_key(
     args: tuple[Hashable, ...],