docs: Add PyTorch .polygamma() tensor operation documentation

content/pytorch/concepts/tensor-operations/terms/polygamma/polygamma.md

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+---
+Title: '.polygamma()'
+Description: 'Computes the n-th derivative of the digamma function for each element in the input tensor.'
+Subjects:
+  - 'AI'
+  - 'Data Science'
+  - 'Machine Learning'
+Tags:
+  - 'Functions'
+  - 'PyTorch'
+  - 'Tensor Operations'
+CatalogContent:
+  - 'intro-to-pytorch'
+  - 'paths/data-science'
+---
+
+The **`.polygamma()`** function in PyTorch computes the polygamma function of input tensors element-wise. The polygamma function is the n-th derivative of the [digamma function](https://www.codecademy.com/resources/docs/pytorch/tensor-operations/digamma), where `n` is a non-negative integer.
+
+## Syntax
+
+```pseudo
+torch.polygamma(n, input, *, out=None) → Tensor
+```
+
+**Parameters:**
+
+- `n` (int): The order of the polygamma function. When `n=0`, this is the digamma function; when `n=1`, this is the trigamma function.
+- `input` (Tensor): The input tensor containing values for which to compute the polygamma function.
+- `out` (Tensor, optional): The output tensor to store the result. Default is `None`.
+
+**Return value:**
+
+A tensor containing the computed polygamma values with the same shape as `input`.
+
+## Example 1: Digamma Function (n=0)
+
+In this example, `.polygamma()` is used with `n=0` to compute the digamma function (first derivative of the log-gamma function):
+
+```py
+import torch
+
+# Create a tensor
+x = torch.tensor([1.0, 2.0, 3.0, 4.0])
+
+# Compute digamma (polygamma with n=0)
+digamma_values = torch.polygamma(0, x)
+print(digamma_values)
+```
+
+The output of this code is:
+
+```shell
+tensor([-0.5772, 0.4228, 0.9228, 1.2561])
+```
+
+## Example 2: Trigamma Function (n=1)
+
+In this example, `.polygamma()` is used with `n=1` to compute the trigamma function (second derivative of the log-gamma function):
+
+```py
+import torch
+
+# Create input tensor
+x = torch.tensor([1.0, 2.0, 3.0])
+
+# Compute trigamma (polygamma with n=1)
+trigamma_values = torch.polygamma(1, x)
+print(trigamma_values)
+```
+
+The output of this code is:
+
+```shell
+tensor([1.6449, 0.6449, 0.3949])
+```
+
+## Example 3: Higher Order Polygamma
+
+In this example, `.polygamma()` is used with `n=2` to compute the second-order polygamma function (derivative of the trigamma function):
+
+```py
+import torch
+
+# Compute polygamma of order 2
+x = torch.tensor([2.0, 3.0, 4.0])
+polygamma_2 = torch.polygamma(2, x)
+print(polygamma_2)
+```
+
+The output of this code is:
+
+```shell
+tensor([-0.8224, -0.3540, -0.2164])
+```