"Fossies" - the Fresh Open Source Software Archive

Source code changes of the file "mpmath/functions/elliptic.py" betweenmpmath-1.0.0.tar.gz and mpmath-1.1.0.tar.gz

About: mpmath is a Python library for arbitrary-precision floating-point arithmetic.

elliptic.py  (mpmath-1.0.0):elliptic.py  (mpmath-1.1.0)
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.. math :: .. math ::
\tau = i \frac{K(1-m)}{K(m)} \tau = i \frac{K(1-m)}{K(m)}
.. math :: .. math ::
q = e^{i \pi \tau} q = e^{i \pi \tau}
.. math :: .. math ::
k = \frac{\vartheta_2^(q)} k = \frac{\vartheta_2^2(q)}{\vartheta_3^2(q)}
In addition, an alternative definition is used for the nome in In addition, an alternative definition is used for the nome in
number theory, which we here denote by q-bar: number theory, which we here denote by q-bar:
.. math :: .. math ::
\bar{q} = q^2 = e^{2 i \pi \tau} \bar{q} = q^2 = e^{2 i \pi \tau}
For convenience, mpmath provides functions to convert For convenience, mpmath provides functions to convert
between the various parameters (:func:~mpmath.qfrom, :func:~mpmath.mfrom, between the various parameters (:func:~mpmath.qfrom, :func:~mpmath.mfrom,
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E\left(\frac{\pi}{2}, m\right) = E(m). E\left(\frac{\pi}{2}, m\right) = E(m).
In the defining integral, it is assumed that the principal branch In the defining integral, it is assumed that the principal branch
of the square root is taken and that the path of integration avoids of the square root is taken and that the path of integration avoids
crossing any branch cuts. Outside -\pi/2 \le \Re(z) \le \pi/2, crossing any branch cuts. Outside -\pi/2 \le \Re(z) \le \pi/2,
the function extends quasi-periodically as the function extends quasi-periodically as
.. math :: .. math ::
E(\phi + n \pi, m) = 2 n E(m) + (\phi,m), n \in \mathbb{Z}. E(\phi + n \pi, m) = 2 n E(m) + E(\phi,m), n \in \mathbb{Z}.
**Plots** **Plots**
.. literalinclude :: /plots/ellipe.py .. literalinclude :: /plots/ellipe.py
.. image :: /plots/ellipe.png .. image :: /plots/ellipe.png
**Examples for the complete integral** **Examples for the complete integral**
Basic values and limits:: Basic values and limits::
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