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+/* specfunc/gsl_sf_dilog.h
+ * 
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 Gerard Jungman
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* Author:  G. Jungman */
+
+#ifndef __GSL_SF_DILOG_H__
+#define __GSL_SF_DILOG_H__
+
+#include <gsl/gsl_sf_result.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+
+/* Real part of DiLogarithm(x), for real argument.
+ * In Lewin's notation, this is Li_2(x).
+ *
+ *   Li_2(x) = - Re[ Integrate[ Log[1-s] / s, {s, 0, x}] ]
+ *
+ * The function in the complex plane has a branch point
+ * at z = 1; we place the cut in the conventional way,
+ * on [1, +infty). This means that the value for real x > 1
+ * is a matter of definition; however, this choice does not
+ * affect the real part and so is not relevant to the
+ * interpretation of this implemented function.
+ */
+int     gsl_sf_dilog_e(const double x, gsl_sf_result * result);
+double  gsl_sf_dilog(const double x);
+
+
+/* DiLogarithm(z), for complex argument z = x + i y.
+ * Computes the principal branch.
+ *
+ * Recall that the branch cut is on the real axis with x > 1.
+ * The imaginary part of the computed value on the cut is given
+ * by -Pi*log(x), which is the limiting value taken approaching
+ * from y < 0. This is a conventional choice, though there is no
+ * true standardized choice.
+ *
+ * Note that there is no canonical way to lift the defining
+ * contour to the full Riemann surface because of the appearance
+ * of a "hidden branch point" at z = 0 on non-principal sheets.
+ * Experts will know the simple algebraic prescription for
+ * obtaining the sheet they want; non-experts will not want
+ * to know anything about it. This is why GSL chooses to compute
+ * only on the principal branch.
+ */
+int
+gsl_sf_complex_dilog_xy_e(
+  const double x,
+  const double y,
+  gsl_sf_result * result_re,
+  gsl_sf_result * result_im
+  );
+
+
+
+/* DiLogarithm(z), for complex argument z = r Exp[i theta].
+ * Computes the principal branch, thereby assuming an
+ * implicit reduction of theta to the range (-2 pi, 2 pi).
+ *
+ * If theta is identically zero, the imaginary part is computed
+ * as if approaching from y > 0. For other values of theta no
+ * special consideration is given, since it is assumed that
+ * no other machine representations of multiples of pi will
+ * produce y = 0 precisely. This assumption depends on some
+ * subtle properties of the machine arithmetic, such as
+ * correct rounding and monotonicity of the underlying
+ * implementation of sin() and cos().
+ *
+ * This function is ok, but the interface is confusing since
+ * it makes it appear that the branch structure is resolved.
+ * Furthermore the handling of values close to the branch
+ * cut is subtle. Perhap this interface should be deprecated.
+ */
+int
+gsl_sf_complex_dilog_e(
+  const double r,
+  const double theta,
+  gsl_sf_result * result_re,
+  gsl_sf_result * result_im
+  );
+
+
+
+/* Spence integral; spence(s) := Li_2(1-s)
+ *
+ * This function has a branch point at 0; we place the
+ * cut on (-infty,0). Because of our choice for the value
+ * of Li_2(z) on the cut, spence(s) is continuous as
+ * s approaches the cut from above. In other words,
+ * we define spence(x) = spence(x + i 0+).
+ */
+int
+gsl_sf_complex_spence_xy_e(
+  const double x,
+  const double y,
+  gsl_sf_result * real_sp,
+  gsl_sf_result * imag_sp
+  );
+
+
+__END_DECLS
+
+#endif /* __GSL_SF_DILOG_H__ */