diff --git a/doc/user_guide/eds.rst b/doc/user_guide/eds.rst
index eee7ce488..6bf2b64c7 100644
--- a/doc/user_guide/eds.rst
+++ b/doc/user_guide/eds.rst
@@ -12,7 +12,7 @@ This chapter describes step-by-step the analysis of an EDS
 spectrum (SEM or TEM).
 
 .. NOTE::
-    See also the `EDS tutorials <https://nbviewer.org/github/hyperspy/hyperspy-demos/tree/main/electron_microscopy/EDS/>`_.
+    See also the `EDS tutorials <https://nbviewer.org/github/hyperspy/exspy-demos/tree/main/EDS/>`_.
 
 Spectrum loading and parameters
 -------------------------------
diff --git a/exspy/components/eels_arctan.py b/exspy/components/eels_arctan.py
index 5a52432bf..4faab579e 100644
--- a/exspy/components/eels_arctan.py
+++ b/exspy/components/eels_arctan.py
@@ -51,12 +51,12 @@ class EELSArctan(hs.model.components1D.Expression):
 
     """
 
-    def __init__(self, A=1.0, k=1.0, x0=1.0, module=["numpy", "scipy"], **kwargs):
+    def __init__(self, A=1.0, k=1.0, x0=1.0, module=["numpy"], **kwargs):
         # To be able to still read old file versions that contain this argument
         if "minimum_at_zero" in kwargs:
             del kwargs["minimum_at_zero"]
         super().__init__(
-            expression="A * (pi /2 + arctan(k * (x - x0)))",
+            expression="A * (pi /2 + atan(k * (x - x0)))",
             name="EELSArctan",
             A=A,
             k=k,
diff --git a/exspy/components/eels_cl_edge.py b/exspy/components/eels_cl_edge.py
index 0a2b91854..3a2f9d8dd 100644
--- a/exspy/components/eels_cl_edge.py
+++ b/exspy/components/eels_cl_edge.py
@@ -75,16 +75,16 @@ class EELSCLEdge(Component):
 
     The preferred option is to use a database of cross sections in GOSH
     format. One such database can be freely downloaded from Zenodo at:
-    https://zenodo.org/record/6599071 while information on the GOSH format
+    https://doi.org/%s while information on the GOSH format
     are available at: https://gitlab.com/gguzzina/gosh .
 
     eXSpy also supports Peter Rez's Hartree Slater cross sections
     parametrised as distributed by Gatan in their Digital Micrograph (DM)
-    software. If Digital Micrograph is installed in the system eXSpy in the
-    standard location eXSpy should find the path to the HS GOS folder.
-    Otherwise, the location of the folder can be defined in eXSpy
-    preferences, which can be done through ~:func:`~.api.preferences.gui` or
-    the :attr:`~api.preferences.EELS.eels_gos_files_path` variable.
+    software. If Digital Micrograph is installed in the system in the
+    standard location, eXSpy should find the path to the HS GOS folder.
+    Otherwise, the location of the folder can be defined in the eXSpy
+    preferences, which can be done through :func:`hyperspy.api.preferences.gui` or
+    the :attr:`hyperspy.api.preferences.EELS.eels_gos_files_path` variable.
 
     Parameters
     ----------
@@ -96,8 +96,8 @@ class EELSCLEdge(Component):
         The GOS to use. Default is ``'gosh'``. If str, it must the path to gosh
         GOS file.
     gos_file_path : str, None
-        Only with GOS='gosh'. Specify the file path of the gosh file
-        to use. If None, use the file from doi:{}
+        Only with ``GOS='gosh'``. Specify the file path of the gosh file
+        to use. If None, use the file from  https://doi.org/%s
 
     Attributes
     ----------
@@ -140,7 +140,7 @@ class EELSCLEdge(Component):
     fine_structure_components : set, default ``set()``
         A set containing components to model the fine structure region
         of the EELS ionization edge.
-    """.format(_GOSH_DOI)
+    """
 
     _fine_structure_smoothing = 0.3
     _fine_structure_coeff_free = True
@@ -290,12 +290,6 @@ def _set_active_fine_structure_components(self, active, **kwargs):
 
     @property
     def fine_structure_smoothing(self):
-        """Controls the level of the smoothing of the fine structure.
-
-        It must a real number between 0 and 1. The higher close to 0
-        the higher the smoothing.
-
-        """
         return self._fine_structure_smoothing
 
     @fine_structure_smoothing.setter
@@ -539,3 +533,6 @@ def as_dictionary(self, fullcopy=True):
         ]
         dic["_whitelist"]["fine_structure_components"] = ""
         return dic
+
+
+EELSCLEdge.__doc__ %= (_GOSH_DOI, _GOSH_DOI)
diff --git a/exspy/components/pes_core_line_shape.py b/exspy/components/pes_core_line_shape.py
index e0484c42d..4480b33c3 100644
--- a/exspy/components/pes_core_line_shape.py
+++ b/exspy/components/pes_core_line_shape.py
@@ -32,7 +32,10 @@ def _calculate_shirley_background(values):
 
 
 class PESCoreLineShape(Component):
-    """ """
+    """
+    Gaussian component with a Shirley background for photoemission
+    spectroscopy analysis.
+    """
 
     def __init__(self, A=1.0, FWHM=1.0, origin=0.0, ab=0.0, shirley=0.0):
         Component.__init__(self, ["A", "FWHM", "origin", "ab", "shirley"])
diff --git a/upcoming_changes/55.bugfix.rst b/upcoming_changes/55.bugfix.rst
new file mode 100644
index 000000000..2c5523ee9
--- /dev/null
+++ b/upcoming_changes/55.bugfix.rst
@@ -0,0 +1 @@
+Fix gradients of the :class:`~.components.EELSArctan` component.
\ No newline at end of file
diff --git a/upcoming_changes/55.doc.rst b/upcoming_changes/55.doc.rst
new file mode 100644
index 000000000..38da8c411
--- /dev/null
+++ b/upcoming_changes/55.doc.rst
@@ -0,0 +1 @@
+Fix broken links in the documentation and missing docstring of the :class:`~.components.PESCoreLineShape` component in the API reference.
\ No newline at end of file