diff --git a/paddle/phi/ops/yaml/python_api_info.yaml b/paddle/phi/ops/yaml/python_api_info.yaml
index c0dffc12dc23a5..e247eb8eed8470 100644
--- a/paddle/phi/ops/yaml/python_api_info.yaml
+++ b/paddle/phi/ops/yaml/python_api_info.yaml
@@ -210,6 +210,16 @@
     x : [input]
     y : [values]
 
+- op : i0
+  name : [paddle.i0,paddle.Tensor.i0]
+  args_alias :
+    use_default_mapping : True
+
+- op : i0e
+  name : [paddle.i0e,paddle.Tensor.i0e]
+  args_alias :
+    use_default_mapping : True
+
 - op : i1
   name : [paddle.i1,paddle.Tensor.i1]
   args_alias :
diff --git a/python/paddle/_paddle_docs.py b/python/paddle/_paddle_docs.py
index 18632753a06025..fdd1e7fc606592 100644
--- a/python/paddle/_paddle_docs.py
+++ b/python/paddle/_paddle_docs.py
@@ -1352,6 +1352,85 @@ def softplus(
 """,
 )
 
+add_doc_and_signature(
+    "i0",
+    """
+    The function used to calculate modified bessel function of order 0.
+
+    Equation:
+        ..  math::
+
+            I_0(x) = \\sum^{\\infty}_{k=0}\frac{(x^2/4)^k}{(k!)^2}
+
+    Args:
+        x (Tensor): The input tensor, it's data type should be float32, float64,
+            uint8, int8, int16, int32, int64.
+        name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
+
+    Returns:
+        - out (Tensor), A Tensor. the value of the modified bessel function of order 0 at x
+            (integer types are autocasted into float32).
+
+    Examples:
+        .. code-block:: python
+
+            >>> import paddle
+
+            >>> x = paddle.to_tensor([0, 1, 2, 3, 4], dtype="float32")
+            >>> paddle.i0(x)
+            Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True,
+            [0.99999994 , 1.26606596 , 2.27958512 , 4.88079262 , 11.30192089])
+    """,
+    """
+    def i0(
+    x: Tensor,
+    name: str | None = None,
+    *,
+    out: Tensor | None = None,
+) -> Tensor
+""",
+)
+
+add_doc_and_signature(
+    "i0e",
+    """
+    The function used to calculate exponentially scaled modified Bessel function of order 0.
+
+    Equation:
+        ..  math::
+
+            I_0(x) = \\sum^{\\infty}_{k=0}\frac{(x^2/4)^k}{(k!)^2} \\
+            I_{0e}(x) = e^{-|x|}I_0(x)
+
+    Args:
+        x (Tensor): The input tensor, it's data type should be float32, float64,
+            uint8, int8, int16, int32, int64.
+        name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
+
+    Returns:
+        - out (Tensor), A Tensor. the value of the exponentially scaled modified Bessel function of order 0 at x
+            (integer types are autocasted into float32).
+
+    Examples:
+        .. code-block:: python
+
+            >>> import paddle
+
+            >>> x = paddle.to_tensor([0, 1, 2, 3, 4], dtype="float32")
+            >>> print(paddle.i0e(x))
+            Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True,
+            [0.99999994, 0.46575963, 0.30850831, 0.24300036, 0.20700191])
+    """,
+    """
+def i0e(
+    x: Tensor,
+    name: str | None = None,
+    *,
+    out: Tensor | None = None,
+) -> Tensor
+""",
+)
+
 add_doc_and_signature(
     "isclose",
     r"""
diff --git a/python/paddle/special.py b/python/paddle/special.py
index 37320ca092d29e..24544d30c5a147 100644
--- a/python/paddle/special.py
+++ b/python/paddle/special.py
@@ -13,10 +13,12 @@
 # limitations under the License.
 
 from .tensor.compat_softmax import softmax
-from .tensor.math import i1, i1e, logsumexp
+from .tensor.math import i0, i0e, i1, i1e, logsumexp
 from .tensor.ops import expm1
 
 __all__ = [
+    "i0",
+    "i0e",
     "i1",
     "i1e",
     "logsumexp",
diff --git a/python/paddle/tensor/math.py b/python/paddle/tensor/math.py
index 219974488230e5..7f5dd8f150a714 100644
--- a/python/paddle/tensor/math.py
+++ b/python/paddle/tensor/math.py
@@ -34,6 +34,8 @@
     fmax,
     fmin,
     heaviside,
+    i0,
+    i0e,
     i1,
     i1e,
     isfinite,
@@ -6190,50 +6192,6 @@ def vander(
     return res
 
 
-def i0(x: Tensor, name: str | None = None) -> Tensor:
-    r"""
-    The function used to calculate modified bessel function of order 0.
-
-    Equation:
-        ..  math::
-
-            I_0(x) = \sum^{\infty}_{k=0}\frac{(x^2/4)^k}{(k!)^2}
-
-    Args:
-        x (Tensor): The input tensor, it's data type should be float32, float64,
-            uint8, int8, int16, int32, int64.
-        name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
-
-    Returns:
-        - out (Tensor), A Tensor. the value of the modified bessel function of order 0 at x
-            (integer types are autocasted into float32).
-
-    Examples:
-        .. code-block:: python
-
-            >>> import paddle
-
-            >>> x = paddle.to_tensor([0, 1, 2, 3, 4], dtype="float32")
-            >>> paddle.i0(x)
-            Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True,
-            [0.99999994 , 1.26606596 , 2.27958512 , 4.88079262 , 11.30192089])
-    """
-    if in_dynamic_or_pir_mode():
-        return _C_ops.i0(x)
-    else:
-        check_variable_and_dtype(
-            x,
-            "x",
-            ["float32", "float64", "uint8", "int8", "int16", "int32", "int64"],
-            "i0",
-        )
-
-        helper = LayerHelper("i0", **locals())
-        out = helper.create_variable_for_type_inference(dtype=x.dtype)
-        helper.append_op(type='i0', inputs={'x': x}, outputs={'out': out})
-    return out
-
-
 @inplace_apis_in_dygraph_only
 def i0_(x: Tensor, name: str | None = None) -> Tensor:
     r"""
@@ -6245,51 +6203,6 @@ def i0_(x: Tensor, name: str | None = None) -> Tensor:
         return _C_ops.i0_(x)
 
 
-def i0e(x: Tensor, name: str | None = None) -> Tensor:
-    r"""
-    The function used to calculate exponentially scaled modified Bessel function of order 0.
-
-    Equation:
-        ..  math::
-
-            I_0(x) = \sum^{\infty}_{k=0}\frac{(x^2/4)^k}{(k!)^2} \\
-            I_{0e}(x) = e^{-|x|}I_0(x)
-
-    Args:
-        x (Tensor): The input tensor, it's data type should be float32, float64,
-            uint8, int8, int16, int32, int64.
-        name (str|None, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None.
-
-    Returns:
-        - out (Tensor), A Tensor. the value of the exponentially scaled modified Bessel function of order 0 at x
-            (integer types are autocasted into float32).
-
-    Examples:
-        .. code-block:: python
-
-            >>> import paddle
-
-            >>> x = paddle.to_tensor([0, 1, 2, 3, 4], dtype="float32")
-            >>> print(paddle.i0e(x))
-            Tensor(shape=[5], dtype=float32, place=Place(cpu), stop_gradient=True,
-            [0.99999994, 0.46575963, 0.30850831, 0.24300036, 0.20700191])
-    """
-    if in_dynamic_or_pir_mode():
-        return _C_ops.i0e(x)
-    else:
-        check_variable_and_dtype(
-            x,
-            "x",
-            ["float32", "float64", "uint8", "int8", "int16", "int32", "int64"],
-            "i0e",
-        )
-
-        helper = LayerHelper("i0e", **locals())
-        out = helper.create_variable_for_type_inference(dtype=x.dtype)
-        helper.append_op(type='i0e', inputs={'x': x}, outputs={'out': out})
-    return out
-
-
 def polygamma(x: Tensor, n: int, name: str | None = None) -> Tensor:
     r"""
     Calculates the polygamma of the given input tensor, element-wise.
diff --git a/test/legacy_test/test_i0_op.py b/test/legacy_test/test_i0_op.py
index deb94dab7e9f15..cfc3cece1bac50 100644
--- a/test/legacy_test/test_i0_op.py
+++ b/test/legacy_test/test_i0_op.py
@@ -159,5 +159,72 @@ def test_check_grad(self):
         self.check_grad(['x'], 'out')
 
 
+class TestI0API_Compatibility(unittest.TestCase):
+    DTYPE = "float64"
+    DATA = [0, 1, 2, 3, 4, 5]
+
+    def setUp(self):
+        self.x = np.array(self.DATA).astype(self.DTYPE)
+        self.out = output_i0(self.x)
+        self.place = get_places()
+
+    def test_dygraph_Compatibility(self):
+        paddle.disable_static()
+        x = paddle.to_tensor(self.x)
+        paddle_dygraph_out = []
+        # Position args (args)
+        out1 = paddle.i0(x)
+        paddle_dygraph_out.append(out1)
+        # Key words args (kwargs) for paddle
+        out2 = paddle.i0(x=x)
+        paddle_dygraph_out.append(out2)
+        # Key words args for torch
+        out3 = paddle.i0(input=x)
+        paddle_dygraph_out.append(out3)
+
+        # Tensor method kwargs
+        out4 = x.i0()
+        paddle_dygraph_out.append(out4)
+        # Test out
+        out5 = paddle.empty([])
+        paddle.i0(x, out=out5)
+        paddle_dygraph_out.append(out5)
+        # scipy reference  out
+        ref_out = output_i0(self.x)
+        # Check
+        for out in paddle_dygraph_out:
+            np.testing.assert_allclose(out.numpy(), ref_out, rtol=1e-5)
+        paddle.enable_static()
+
+    def test_static_Compatibility(self):
+        def run(place):
+            paddle.enable_static()
+            with paddle.static.program_guard(paddle.static.Program()):
+                x = paddle.static.data(
+                    name="x", shape=self.x.shape, dtype=self.DTYPE
+                )
+                # Position args (args)
+                out1 = paddle.i0(x)
+                # Key words args (kwargs) for paddle
+                out2 = paddle.i0(x=x)
+                # Key words args for torch
+                out3 = paddle.i0(input=x)
+                # Tensor method args
+                out4 = x.i0()
+
+                exe = paddle.static.Executor(place)
+                fetches = exe.run(
+                    paddle.static.default_main_program(),
+                    feed={"x": self.x},
+                    fetch_list=[out1, out2, out3, out4],
+                )
+                for out in fetches:
+                    np.testing.assert_allclose(out, self.out, rtol=1e-5)
+            paddle.disable_static()
+
+        for place in self.place:
+            run(place)
+
+
 if __name__ == "__main__":
     unittest.main()
diff --git a/test/legacy_test/test_i0e_op.py b/test/legacy_test/test_i0e_op.py
index fef8911939fc99..4f4d8d55ec0ab9 100644
--- a/test/legacy_test/test_i0e_op.py
+++ b/test/legacy_test/test_i0e_op.py
@@ -163,5 +163,72 @@ def test_check_grad(self):
         self.check_grad(['x'], 'out')
 
 
+class TestI0eAPI_Compatibility(unittest.TestCase):
+    DTYPE = "float64"
+    DATA = [0, 1, 2, 3, 4, 5]
+
+    def setUp(self):
+        self.x = np.array(self.DATA).astype(self.DTYPE)
+        self.out = output_i0e(self.x)
+        self.place = get_places()
+
+    def test_dygraph_Compatibility(self):
+        paddle.disable_static()
+        x = paddle.to_tensor(self.x)
+        paddle_dygraph_out = []
+        # Position args (args)
+        out1 = paddle.i0e(x)
+        paddle_dygraph_out.append(out1)
+        # Key words args (kwargs) for paddle
+        out2 = paddle.i0e(x=x)
+        paddle_dygraph_out.append(out2)
+        # Key words args for torch
+        out3 = paddle.i0e(input=x)
+        paddle_dygraph_out.append(out3)
+
+        # Tensor method kwargs
+        out4 = x.i0e()
+        paddle_dygraph_out.append(out4)
+        # Test out
+        out5 = paddle.empty([])
+        paddle.i0e(x, out=out5)
+        paddle_dygraph_out.append(out5)
+        # scipy reference  out
+        ref_out = output_i0e(self.x)
+        # Check
+        for out in paddle_dygraph_out:
+            np.testing.assert_allclose(out.numpy(), ref_out, rtol=1e-5)
+        paddle.enable_static()
+
+    def test_static_Compatibility(self):
+        def run(place):
+            paddle.enable_static()
+            with paddle.static.program_guard(paddle.static.Program()):
+                x = paddle.static.data(
+                    name="x", shape=self.x.shape, dtype=self.DTYPE
+                )
+                # Position args (args)
+                out1 = paddle.i0e(x)
+                # Key words args (kwargs) for paddle
+                out2 = paddle.i0e(x=x)
+                # Key words args for torch
+                out3 = paddle.i0e(input=x)
+                # Tensor method args
+                out4 = x.i0e()
+
+                exe = paddle.static.Executor(place)
+                fetches = exe.run(
+                    paddle.static.default_main_program(),
+                    feed={"x": self.x},
+                    fetch_list=[out1, out2, out3, out4],
+                )
+                for out in fetches:
+                    np.testing.assert_allclose(out, self.out, rtol=1e-5)
+            paddle.disable_static()
+
+        for place in self.place:
+            run(place)
+
+
 if __name__ == "__main__":
     unittest.main()