diff --git a/src/beignet/special/_dawson_integral_f.py b/src/beignet/special/_dawson_integral_f.py
index a6aed878cc..e1cf5e190a 100644
--- a/src/beignet/special/_dawson_integral_f.py
+++ b/src/beignet/special/_dawson_integral_f.py
@@ -7,4 +7,13 @@
 
 
 def dawson_integral_f(input: Tensor) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    input : Tensor
+
+    Returns
+    -------
+    Tensor
+    """
     return math.sqrt(torch.pi) / 2.0 * torch.exp(-(input**2)) * error_erfi(input)
diff --git a/src/beignet/special/_error_erf.py b/src/beignet/special/_error_erf.py
index ad701532c8..4b41d2c7cd 100644
--- a/src/beignet/special/_error_erf.py
+++ b/src/beignet/special/_error_erf.py
@@ -4,4 +4,15 @@
 
 
 def error_erf(input: Tensor) -> Tensor:
+    r"""
+    Error function.
+
+    Parameters
+    ----------
+    input : Tensor
+
+    Returns
+    -------
+    Tensor
+    """
     return 1.0 - error_erfc(input)
diff --git a/src/beignet/special/_error_erfc.py b/src/beignet/special/_error_erfc.py
index e687da4651..706890e19a 100644
--- a/src/beignet/special/_error_erfc.py
+++ b/src/beignet/special/_error_erfc.py
@@ -5,4 +5,15 @@
 
 
 def error_erfc(input: Tensor) -> Tensor:
+    r"""
+    Complementary error function.
+
+    Parameters
+    ----------
+    input : Tensor
+
+    Returns
+    -------
+    Tensor
+    """
     return torch.exp(-torch.pow(input, 2)) * faddeeva_w(1.0j * input)
diff --git a/src/beignet/special/_error_erfi.py b/src/beignet/special/_error_erfi.py
index d8078f08af..ce372a853b 100644
--- a/src/beignet/special/_error_erfi.py
+++ b/src/beignet/special/_error_erfi.py
@@ -4,11 +4,12 @@
 
 
 def error_erfi(input: Tensor) -> Tensor:
-    r"""Imaginary error function.
+    r"""
+    Imaginary error function.
 
     Parameters
     ----------
-    input: Tensor
+    input : Tensor
 
     Returns
     -------
diff --git a/src/beignet/special/_faddeeva_w.py b/src/beignet/special/_faddeeva_w.py
index c7bb9d4cb9..d721d5d170 100644
--- a/src/beignet/special/_faddeeva_w.py
+++ b/src/beignet/special/_faddeeva_w.py
@@ -159,19 +159,15 @@ def _faddeeva_w_impl(z):
     return _voigt_v_impl(z.real, z.imag) + 1j * _voigt_l_impl(z.real, z.imag)
 
 
-def faddeeva_w(input: Tensor):
-    r"""Compute faddeeva w function using method described in [1].
-
+def faddeeva_w(input: Tensor) -> Tensor:
+    r"""
     Parameters
     ----------
-    input: Tensor
-        complex input
+    input : Tensor
 
-    References
-    ----------
-    [1] Al Azah, Mohammad, and Simon N. Chandler-Wilde.
-        "Computation of the complex error function using modified trapezoidal rules."
-        SIAM Journal on Numerical Analysis 59.5 (2021): 2346-2367.
+    Returns
+    -------
+    Tensor
     """
     # use symmetries to map to upper right quadrant of complex plane
     imag_negative = input.imag < 0.0