To fix the tests, a "cdef extern from" was used.

docs/examples/memoryviews/C_func_file.c

+#include "C_func_file.h"
+
 void multiply_by_10_in_C(double arr[], unsigned int n)
 {
     for (int i = 0; i < n; i++) {

docs/examples/memoryviews/C_func_file.h

+#ifndef C_FUNC_FILE_H
+#define C_FUNC_FILE_H
+
 void multiply_by_10_in_C(double arr[], unsigned int n);
+
+#endif

docs/examples/memoryviews/memview_to_c.pyx

-# distutils: sources = C_func_file.c
-# distutils: include_dirs = ./
+cdef extern from "C_func_file.c":
+    # C is include here so that it doesn't need to be compiled externally
+    pass
 
 cdef extern from "C_func_file.h":
     void multiply_by_10_in_C(double *, unsigned int)

docs/src/userguide/memoryviews.rst

@@ -706,9 +706,10 @@ array with an external C function implemented in :file:`C_func_file.c`:
 .. literalinclude:: ../../examples/memoryviews/C_func_file.c
     :linenos:
 
-This file comes with a header file called :file:`C_func_file.h` containing::
+This file comes with a header file called :file:`C_func_file.h` containing:
 
-    void multiply_by_10_in_C(double arr[], unsigned int n);
+.. literalinclude:: ../../examples/memoryviews/C_func_file.h
+    :linenos:
 
 where ``arr`` points to the array and ``n`` is its size.