docs: expand landing page with sample notebooks

Expands the BigQuery DataFrames landing page with interactive sample
notebooks (direct links to Consumer Colab and BigQuery Studio) and
curated articles.

Summary of Changes:
- Added sample notebooks list-table with direct Colab and BigQuery Studio links.
- Added articles and guides section linking to official blogs and documentation.
- Highlighted Generative AI capabilities via bigframes.bigquery.ai.

Fixes: 522964184

Change-Id: I3a9307e118293bdb879ad9e1cd4eaefca2257c36
Reviewed-on: https://bigframes-internal-review.git.corp.google.com/c/bigframes/+/4061
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Reviewed-by: Shenyang Cai <sycai@google.com>
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Author: shuoweil

docs/index.rst

@@ -15,7 +15,7 @@ BigFrames eliminates the "data movement bottleneck." Instead of downloading larg
 
 *   **Petabyte-Scale Scalability:** Effortlessly process datasets that far exceed local memory limits.
 *   **Familiar Python Ecosystem:** Use the same ``read_gbq``, ``groupby``, ``merge``, and ``pivot_table`` functions you already know from pandas.
-*   **Integrated Machine Learning:** Access BigQuery ML's powerful algorithms via a scikit-learn-like interface (``bigframes.ml``), including seamless **Gemini AI** integration.
+*   **Generative AI and Machine Learning:** Seamlessly leverage Gemini models, AI functions, and vector search with :mod:`bigframes.bigquery.ai`, alongside BigQuery ML's powerful algorithms via a scikit-learn-compatible interface (``bigframes.ml``).
 *   **Enterprise-Grade Security:** Maintain data governance and security by keeping your data within the BigQuery perimeter.
 *   **Hybrid Flexibility:** Easily move between distributed BigQuery processing and local pandas analysis with ``to_pandas()``.
 
@@ -62,6 +62,62 @@ The following example demonstrates how to perform a distributed aggregation on a
     print(top_names.to_pandas())
 
 
+Sample Notebooks and Interactive Demos
+--------------------------------------
+
+Explore sample notebooks demonstrating end-to-end workflows across analytics, GenAI, and machine learning. Each notebook can be launched directly in **BigQuery Studio** or **Consumer Colab**:
+
+.. list-table::
+   :widths: 40 30 30
+   :header-rows: 1
+
+   * - Notebook
+     - BigQuery Studio
+     - Consumer Colab
+   * - **Getting started with BigFrames**
+     - `Open in BQ Studio <https://console.cloud.google.com/bigquery/import?url=https://github.com/google/bigframes/blob/main/notebooks/getting_started/bq_dataframes_template.ipynb>`__
+     - `Run in Colab <https://colab.research.google.com/github/google/bigframes/blob/main/notebooks/getting_started/bq_dataframes_template.ipynb>`__
+   * - **AI functions (Gemini & GenAI)**
+     - `Open in BQ Studio <https://console.cloud.google.com/bigquery/import?url=https://github.com/google/bigframes/blob/main/notebooks/generative_ai/ai_functions.ipynb>`__
+     - `Run in Colab <https://colab.research.google.com/github/google/bigframes/blob/main/notebooks/generative_ai/ai_functions.ipynb>`__
+   * - **Data visualization**
+     - `Open in BQ Studio <https://console.cloud.google.com/bigquery/import?url=https://github.com/google/bigframes/blob/main/notebooks/visualization/tutorial.ipynb>`__
+     - `Run in Colab <https://colab.research.google.com/github/google/bigframes/blob/main/notebooks/visualization/tutorial.ipynb>`__
+   * - **Analyzing posters with AI functions**
+     - `Open in BQ Studio <https://console.cloud.google.com/bigquery/import?url=https://github.com/google/bigframes/blob/main/notebooks/generative_ai/ai_movie_poster.ipynb>`__
+     - `Run in Colab <https://colab.research.google.com/github/google/bigframes/blob/main/notebooks/generative_ai/ai_movie_poster.ipynb>`__
+   * - **DataFrame operations**
+     - `Open in BQ Studio <https://console.cloud.google.com/bigquery/import?url=https://github.com/google/bigframes/blob/main/notebooks/dataframes/dataframe.ipynb>`__
+     - `Run in Colab <https://colab.research.google.com/github/google/bigframes/blob/main/notebooks/dataframes/dataframe.ipynb>`__
+   * - **Multimodal DataFrames**
+     - `Open in BQ Studio <https://console.cloud.google.com/bigquery/import?url=https://github.com/google/bigframes/blob/main/notebooks/multimodal/multimodal_dataframe.ipynb>`__
+     - `Run in Colab <https://colab.research.google.com/github/google/bigframes/blob/main/notebooks/multimodal/multimodal_dataframe.ipynb>`__
+   * - **SQL interoperability with bqsql magic**
+     - `Open in BQ Studio <https://console.cloud.google.com/bigquery/import?url=https://github.com/google/bigframes/blob/main/notebooks/dataframes/magics_with_local_data.ipynb>`__
+     - `Run in Colab <https://colab.research.google.com/github/google/bigframes/blob/main/notebooks/dataframes/magics_with_local_data.ipynb>`__
+   * - **Timedelta operations**
+     - `Open in BQ Studio <https://console.cloud.google.com/bigquery/import?url=https://github.com/google/bigframes/blob/main/notebooks/data_types/timedelta.ipynb>`__
+     - `Run in Colab <https://colab.research.google.com/github/google/bigframes/blob/main/notebooks/data_types/timedelta.ipynb>`__
+   * - **Remote Functions**
+     - `Open in BQ Studio <https://console.cloud.google.com/bigquery/import?url=https://github.com/google/bigframes/blob/main/notebooks/remote_functions/remote_function.ipynb>`__
+     - `Run in Colab <https://colab.research.google.com/github/google/bigframes/blob/main/notebooks/remote_functions/remote_function.ipynb>`__
+
+Browse the `complete notebooks catalog on GitHub <https://github.com/google/bigframes/tree/main/notebooks>`_ for additional tutorials and community examples.
+
+
+Articles and Guides
+-------------------
+
+To learn more about BigQuery DataFrames architecture, features, and best practices, check out the following articles and documentation guides:
+
+*   `BigQuery DataFrames: Generally Available <https://cloud.google.com/blog/products/data-analytics/bigquery-dataframes-generally-available>`_: Official announcement detailing petabyte-scale pandas and scikit-learn on BigQuery.
+*   `Generative AI in BigQuery with DataFrames <https://cloud.google.com/blog/products/data-analytics/generative-ai-in-bigquery-with-dataframes>`_: How to leverage Gemini models and AI functions directly in Python.
+*   `Analyze Multimodal Data with BigQuery DataFrames <https://cloud.google.com/blog/products/data-analytics/analyze-multimodal-data-with-bigquery-dataframes>`_: End-to-end unstructured data analysis across images, audio, and PDF documents.
+*   `Scalable Data Science with BigQuery DataFrames <https://cloud.google.com/blog/products/data-analytics/data-science-with-bigquery-dataframes>`_: Best practices for scaling analytics and machine learning workflows in the cloud.
+*   `BigQuery DataFrames Introduction (Cloud Docs) <https://cloud.google.com/bigquery/docs/bigquery-dataframes-introduction>`_: Official documentation covering data manipulation, sessions, and deployment.
+*   `Try BigQuery DataFrames (Quickstart Guide) <https://cloud.google.com/bigquery/docs/dataframes-quickstart>`_: Step-by-step tutorial in BigQuery Studio and Colab.
+
+
 Explore the Documentation
 -------------------------