.. _sphx_glr_api_gallery_special_functions_hypergeometric:

Hypergeometric functions
------------------------

Gauss's hypergeometric function and Kummer's confluent hypergeometric function.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Recovers log(1 + z), arcsin z, and a Chebyshev polynomial from 2F1 with special parameters, and checks Gauss&#x27;s summation theorem at z = 1.">

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  .. image:: /api/gallery/special_functions/hypergeometric/images/thumb/sphx_glr_plot_01_gauss_hypergeometric_thumb.png
    :alt:

  :doc:`/api/gallery/special_functions/hypergeometric/plot_01_gauss_hypergeometric`

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      <div class="sphx-glr-thumbnail-title">Gauss's hypergeometric function contains the elementary functions</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Checks Kummer&#x27;s transformation M(a, b, z) = e^z M(b - a, b, -z) and shows 2F1(a, c; b; z/c) merging into 1F1(a; b; z) as c grows.">

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  .. image:: /api/gallery/special_functions/hypergeometric/images/thumb/sphx_glr_plot_02_kummer_confluent_thumb.png
    :alt:

  :doc:`/api/gallery/special_functions/hypergeometric/plot_02_kummer_confluent`

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      <div class="sphx-glr-thumbnail-title">Kummer's confluent hypergeometric function</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/special_functions/hypergeometric/plot_01_gauss_hypergeometric
   /api/gallery/special_functions/hypergeometric/plot_02_kummer_confluent