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+---
+Title: '.i0()'
+Description: 'Computes the modified Bessel function of the first kind of order zero.'
+Subjects:
+  - 'AI'
+  - 'Data Science'
+  - 'Machine Learning'
+Tags:
+  - 'AI'
+  - 'Deep Learning'
+  - 'Functions'
+  - 'Machine Learning'
+  - 'PyTorch'
+CatalogContent:
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'paths/computer-science'
+---
+
+In PyTorch, the **`.i0()`** function (an alias of `torch.special.i0()`) computes the modified Bessel function of the first kind of order zero (I₀). This function is commonly used in signal processing, physics simulations, and statistical distributions such as the von Mises distribution for circular data.
+
+## Syntax
+
+```pseudo
+torch.i0(input, *, out=None)
+```
+
+Or, alternatively:
+
+```pseudo
+torch.special.i0(input, *, out=None)
+```
+
+**Parameters:**
+
+- `input` (Tensor): The input tensor whose elements are the values at which to compute the modified Bessel function I₀.
+- `out` (Tensor, optional): The output tensor to store the result.
+
+**Return value:**
+
+Returns a tensor containing the computed modified Bessel function of the first kind, order zero (I₀), for each element of the input tensor.
+
+## Example
+
+In this example, `torch.i0()` calculates the modified Bessel function I₀ for each element in a 1D tensor:
+
+```py
+import torch
+
+# Create input tensor
+x = torch.tensor([0.0, 1.0, 2.0, 3.0, 4.0])
+
+# Compute the modified Bessel function
+result = torch.i0(x)
+
+print("Input values:", x)
+print("I₀(x) values:", result)
+```
+
+The above code produces the following output:
+
+```shell
+Input values: tensor([0., 1., 2., 3., 4.])
+I₀(x) values: tensor([1.0000, 1.2661, 2.2796, 4.8808, 11.3019])
+```