Blame doc/specfunc-dilog.rst
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.. index:: dilogarithm
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The dilogarithm is defined as
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.. only:: not texinfo
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.. math:: Li_2(z) = - \int_0^z ds {\log{(1-s)} \over s}
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.. only:: texinfo
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.. math:: Li_2(z) = - \int_0^z ds log(1-s) / s
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The functions described in this section are declared in the header file
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:file:`gsl_sf_dilog.h`.
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Real Argument
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-------------
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.. function:: double gsl_sf_dilog (double x)
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int gsl_sf_dilog_e (double x, gsl_sf_result * result)
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These routines compute the dilogarithm for a real argument. In Lewin's
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notation this is :math:`Li_2(x)`, the real part of the dilogarithm of a
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real :math:`x`. It is defined by the integral representation
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.. math:: Li_2(x) = - \Re \int_0^x ds \log(1-s) / s
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Note that :math:`\Im(Li_2(x)) = 0` for
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:math:`x \le 1`, and :math:`-\pi\log(x)` for :math:`x > 1`.
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Note that Abramowitz & Stegun refer to the Spence integral
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:math:`S(x) = Li_2(1 - x)` as the dilogarithm rather than :math:`Li_2(x)`.
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Complex Argument
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----------------
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.. function:: int gsl_sf_complex_dilog_e (double r, double theta, gsl_sf_result * result_re, gsl_sf_result * result_im)
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This function computes the full complex-valued dilogarithm for the
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complex argument :math:`z = r \exp(i \theta)`. The real and imaginary
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parts of the result are returned in :data:`result_re`, :data:`result_im`.
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