.. _sphx_glr_api_gallery_special_functions_gamma_beta:

Gamma and beta functions
---------------------------

The gamma and beta functions, and Stirling's approximation.


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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="Confirms Gamma(n) = (n-1)! at integers, Gamma(1/2) = sqrt(pi), and the beta function&#x27;s relationship to gamma.">

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  .. image:: /api/gallery/special_functions/gamma_beta/images/thumb/sphx_glr_plot_01_gamma_extends_factorial_thumb.png
    :alt:

  :doc:`/api/gallery/special_functions/gamma_beta/plot_01_gamma_extends_factorial`

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      <div class="sphx-glr-thumbnail-title">The gamma function extends the factorial</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Shows that sqrt(2 pi n) (n/e)^n approximates n! with relative error about 1/(12n), and that Stirling&#x27;s full series for log Gamma(x) is asymptotic: at small x, adding terms first helps and then hurts.">

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  .. image:: /api/gallery/special_functions/gamma_beta/images/thumb/sphx_glr_plot_02_stirling_formula_thumb.png
    :alt:

  :doc:`/api/gallery/special_functions/gamma_beta/plot_02_stirling_formula`

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      <div class="sphx-glr-thumbnail-title">Stirling's formula and its asymptotic series</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/special_functions/gamma_beta/plot_01_gamma_extends_factorial
   /api/gallery/special_functions/gamma_beta/plot_02_stirling_formula