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Weierstrass elliptic functions, in terms of elliptic period ratio `\tau`
=======================================================================================================



Weierstrass function `\wp(z| \tau)`
-------------------------------------------------------------------------------

Some Text


|02a_TestEllk_re1| `\quad` |02b_TestEllk_im1| `\quad` |02c_TestEllk_abs1|

.. |02a_TestEllk_re1| image:: ../_static/ExplicitSurfaces/CplxElliptic/02a_TestEllk_re.3D.xml.jpg
    :width: 30 %

.. |02b_TestEllk_im1| image:: ../_static/ExplicitSurfaces/CplxElliptic/02b_TestEllk_im.3D.xml.jpg
    :width: 30 %

.. |02c_TestEllk_abs1| image:: ../_static/ExplicitSurfaces/CplxElliptic/02c_TestEllk_abs.3D.xml.jpg
    :width: 30 %

   

**3D wpf plot**: real part (left figure), imaginary part (middle figure) and absolute value with color-coded phase (right figure) of the complex sine function `z = \sin(x + iy)`, with `-6 \le x \le 6` (blue axis), `-6 \le y \le 6` (red axis), `-10 \le z \le 10` (green axis). Function values are :ref:`loglog-transformed <rst_mpm_loglog_transformation>`.






Weierstrass function, first derivative: `\wp'z| \tau)`
-------------------------------------------------------------------------------


Some Text


|02a_TestEllk_re2| `\quad` |02b_TestEllk_im2| `\quad` |02c_TestEllk_abs2|

.. |02a_TestEllk_re2| image:: ../_static/ExplicitSurfaces/CplxElliptic/02a_TestEllk_re.3D.xml.jpg
    :width: 30 %

.. |02b_TestEllk_im2| image:: ../_static/ExplicitSurfaces/CplxElliptic/02b_TestEllk_im.3D.xml.jpg
    :width: 30 %

.. |02c_TestEllk_abs2| image:: ../_static/ExplicitSurfaces/CplxElliptic/02c_TestEllk_abs.3D.xml.jpg
    :width: 30 %

   

**3D wpf plot**: real part (left figure), imaginary part (middle figure) and absolute value with color-coded phase (right figure) of the complex sine function `z = \sin(x + iy)`, with `-6 \le x \le 6` (blue axis), `-6 \le y \le 6` (red axis), `-10 \le z \le 10` (green axis). Function values are :ref:`loglog-transformed <rst_mpm_loglog_transformation>`.






Inverse Weierstrass function `\wp^{-1}(z| \tau)`
-------------------------------------------------------------------------------


Some Text


|02a_TestEllk_re3| `\quad` |02b_TestEllk_im3| `\quad` |02c_TestEllk_abs3|

.. |02a_TestEllk_re3| image:: ../_static/ExplicitSurfaces/CplxElliptic/02a_TestEllk_re.3D.xml.jpg
    :width: 30 %

.. |02b_TestEllk_im3| image:: ../_static/ExplicitSurfaces/CplxElliptic/02b_TestEllk_im.3D.xml.jpg
    :width: 30 %

.. |02c_TestEllk_abs3| image:: ../_static/ExplicitSurfaces/CplxElliptic/02c_TestEllk_abs.3D.xml.jpg
    :width: 30 %



**3D wpf plot**: real part (left figure), imaginary part (middle figure) and absolute value with color-coded phase (right figure) of the complex sine function `z = \sin(x + iy)`, with `-6 \le x \le 6` (blue axis), `-6 \le y \le 6` (red axis), `-10 \le z \le 10` (green axis). Function values are :ref:`loglog-transformed <rst_mpm_loglog_transformation>`.









Weierstrass Zeta function `\zeta(z, \tau)`
-------------------------------------------------------------------------------


Some Text


|02a_TestEllk_re4| `\quad` |02b_TestEllk_im4| `\quad` |02c_TestEllk_abs4|

.. |02a_TestEllk_re4| image:: ../_static/ExplicitSurfaces/CplxElliptic/02a_TestEllk_re.3D.xml.jpg
    :width: 30 %

.. |02b_TestEllk_im4| image:: ../_static/ExplicitSurfaces/CplxElliptic/02b_TestEllk_im.3D.xml.jpg
    :width: 30 %

.. |02c_TestEllk_abs4| image:: ../_static/ExplicitSurfaces/CplxElliptic/02c_TestEllk_abs.3D.xml.jpg
    :width: 30 %



**3D wpf plot**: real part (left figure), imaginary part (middle figure) and absolute value with color-coded phase (right figure) of the complex sine function `z = \sin(x + iy)`, with `-6 \le x \le 6` (blue axis), `-6 \le y \le 6` (red axis), `-10 \le z \le 10` (green axis). Function values are :ref:`loglog-transformed <rst_mpm_loglog_transformation>`.








Weierstrass Sigma function `\sigma(z| \tau)`
-------------------------------------------------------------------------------



Some Text


|02a_TestEllk_re5| `\quad` |02b_TestEllk_im5| `\quad` |02c_TestEllk_abs5|

.. |02a_TestEllk_re5| image:: ../_static/ExplicitSurfaces/CplxElliptic/02a_TestEllk_re.3D.xml.jpg
    :width: 30 %

.. |02b_TestEllk_im5| image:: ../_static/ExplicitSurfaces/CplxElliptic/02b_TestEllk_im.3D.xml.jpg
    :width: 30 %

.. |02c_TestEllk_abs5| image:: ../_static/ExplicitSurfaces/CplxElliptic/02c_TestEllk_abs.3D.xml.jpg
    :width: 30 %



**3D wpf plot**: real part (left figure), imaginary part (middle figure) and absolute value with color-coded phase (right figure) of the complex sine function `z = \sin(x + iy)`, with `-6 \le x \le 6` (blue axis), `-6 \le y \le 6` (red axis), `-10 \le z \le 10` (green axis). Function values are :ref:`loglog-transformed <rst_mpm_loglog_transformation>`.