.. _sphx_glr_api_gallery_special_functions_error_functions:

Error function and Fresnel integrals
------------------------------------

Gaussian integrals along the real axis and along the diagonal of the complex plane.


.. raw:: html

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


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

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Draws the Euler-Cornu spiral (C(t), S(t)), which winds into the points (1/2, 1/2) and (-1/2, -1/2), and the knife-edge diffraction intensity that Fresnel computed from it.">

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  .. image:: /api/gallery/special_functions/error_functions/images/thumb/sphx_glr_plot_01_fresnel_cornu_spiral_thumb.png
    :alt:

  :doc:`/api/gallery/special_functions/error_functions/plot_01_fresnel_cornu_spiral`

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      <div class="sphx-glr-thumbnail-title">Fresnel integrals and the Cornu spiral</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Recovers the 68-95-99.7 rule from erf, and shows why erfc is needed in the far tail, where 1 - erf(x) rounds to zero.">

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  .. image:: /api/gallery/special_functions/error_functions/images/thumb/sphx_glr_plot_02_error_function_thumb.png
    :alt:

  :doc:`/api/gallery/special_functions/error_functions/plot_02_error_function`

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      <div class="sphx-glr-thumbnail-title">The error function and the normal distribution</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/special_functions/error_functions/plot_01_fresnel_cornu_spiral
   /api/gallery/special_functions/error_functions/plot_02_error_function