diff --git a/spec/API_specification/constants.md b/spec/API_specification/constants.md
new file mode 100644
index 000000000..acb214ef0
--- /dev/null
+++ b/spec/API_specification/constants.md
@@ -0,0 +1,31 @@
+# Constants
+
+> Array API specification for constants.
+
+A conforming implementation of the array API standard must provide and support the following constants.
+
+<!-- NOTE: please keep the constants in alphabetical order -->
+
+### <a name="e" href="#e">#</a> e
+
+Euler's constant.
+
+```text
+e = 2.71828182845904523536028747135266249775724709369995...
+```
+
+### <a name="inf" href="#inf">#</a> inf
+
+IEEE 754 floating point representation of (positive) infinity.
+
+### <a name="nan" href="#nan">#</a> nan
+
+IEEE 754 floating point representation of Not a Number (`NaN`).
+
+### <a name="pi" href="#pi">#</a> pi
+
+The mathematical constant `π`.
+
+```text
+pi = 3.1415926535897932384626433...
+```
\ No newline at end of file
diff --git a/spec/API_specification/elementwise_functions.md b/spec/API_specification/elementwise_functions.md
index 23eb56379..d9e1ff6e4 100644
--- a/spec/API_specification/elementwise_functions.md
+++ b/spec/API_specification/elementwise_functions.md
@@ -431,6 +431,54 @@ Computes the truth value of `x1_i >= x2_i` for each element `x1_i` of the input
 
     -   an array containing the element-wise results.
 
+### <a name="isfinite" href="#isfinite">#</a> isfinite(x, /)
+
+Tests each element `x_i` of the input array `x` to determine if finite (i.e., not `NaN` and not equal to positive or negative infinity).
+
+#### Parameters
+
+-   **x**: _&lt;array&gt;_
+
+    -   input array.
+
+#### Returns
+
+-   **out**: _&lt;array&gt;_
+
+    -   an array, whose underlying data type is `bool`, containing test results. An element `out_i` is `True` if `x_i` is finite and `False` otherwise.
+
+### <a name="isinf" href="#isinf">#</a> isinf(x, /)
+
+Tests each element `x_i` of the input array `x` to determine if equal to positive or negative infinity.
+
+#### Parameters
+
+-   **x**: _&lt;array&gt;_
+
+    -   input array.
+
+#### Returns
+
+-   **out**: _&lt;array&gt;_
+
+    -   an array, whose underlying data type is `bool`, containing test results. An element `out_i` is `True` if `x_i` is either positive or negative infinity and `False` otherwise.
+
+### <a name="isnan" href="#isnan">#</a> isnan(x, /)
+
+Tests each element `x_i` of the input array `x` to determine whether the element is `NaN`.
+
+#### Parameters
+
+-   **x**: _&lt;array&gt;_
+
+    -   input array.
+
+#### Returns
+
+-   **out**: _&lt;array&gt;_
+
+    -   an array, whose underlying data type is `bool`, containing test results. An element `out_i` is `True` if `x_i` is `NaN` and `False` otherwise.
+
 ### <a name="less" href="#less">#</a> less(x1, x2, /)
 
 Computes the truth value of `x1_i < x2_i` for each element `x1_i` of the input array `x1` with the respective element `x2_i` of the input array `x2`.
diff --git a/spec/API_specification/index.rst b/spec/API_specification/index.rst
index 3d16132df..46b7c9366 100644
--- a/spec/API_specification/index.rst
+++ b/spec/API_specification/index.rst
@@ -19,3 +19,4 @@ API specification
    linear_algebra_functions
    searching_functions
    set_functions
+   constants