Specify special case in terms of cis function

Author: kgryte

spec/API_specification/array_api/elementwise_functions.py

@@ -537,8 +537,8 @@ def exp(x: array, /) -> array:
     - If ``a`` is a finite number and ``b`` is ``+infinity``, the result is ``NaN + NaN j``.
     - If ``a`` is a finite number and ``b`` is ``NaN``, the result is ``NaN + NaN j``.
     - If ``a`` is ``+infinity`` and ``b`` is either ``+0`` or ``-0``, the result is ``infinity + 0j``.
-    - If ``a`` is ``-infinity`` and ``b`` is a finite number, the result is ``0 + 0j``.
-    - If ``a`` is ``+infinity`` and ``b`` is a nonzero finite number, the result is ``infinity + infinity j``.
+    - If ``a`` is ``-infinity`` and ``b`` is a finite number, the result is ``+0 * cis(x_i)``.
+    - If ``a`` is ``+infinity`` and ``b`` is a nonzero finite number, the result is ``+infinity * cis(x_i)``.
     - If ``a`` is ``-infinity`` and ``b`` is ``+infinity``, the result is ``0 + 0j`` (signs of real and imaginary components are unspecified).
     - If ``a`` is ``+infinity`` and ``b`` is ``+infinity``, the result is ``infinity + NaN j`` (sign of real component is unspecified).
     - If ``a`` is ``-infinity`` and ``b`` is ``NaN``, the result is ``0 + 0j`` (signs of real and imaginary components are unspecified).
@@ -547,6 +547,8 @@ def exp(x: array, /) -> array:
     - If ``a`` is ``NaN`` and ``b`` is not equal to ``0``, the result is ``NaN + NaN j``.
     - If ``a`` is ``NaN`` and ``b`` is ``NaN``, the result is ``NaN + NaN j``.
 
+    where ``cis(x_i)`` is ``cos(x_i) + sin(x_i)*1j``.
+
     .. note::
        The exponential function is an entire function in the complex plane and has no branch cuts.