int order,
unsigned options)
{
+ GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol));
// method:
// Taylor series where there is no pole falls back to tan_deriv.
// On a pole simply expand sin(x)/cos(x).
if (!(2*x_pt/Pi).info(info_flags::odd))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole
- return (sin(x)/cos(x)).series(rel, order+2);
+ return (sin(x)/cos(x)).series(rel, order+2, options);
}
REGISTER_FUNCTION(tan, eval_func(tan_eval).
return power(_ex1()+power(x,_ex2()), _ex_1());
}
+static ex atan_series(const ex &x,
+ const relational &rel,
+ int order,
+ unsigned options)
+{
+ GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol));
+ // method:
+ // Taylor series where there is no pole or cut falls back to atan_deriv.
+ // There are two branch cuts, one runnig from I up the imaginary axis and
+ // one running from -I down the imaginary axis. The points I and -I are
+ // poles.
+ // On the branch cuts and the poles series expand
+ // log((1+I*x)/(1-I*x))/(2*I)
+ // instead.
+ // (The constant term on the cut itself could be made simpler.)
+ const ex x_pt = x.subs(rel);
+ if (!(I*x_pt).info(info_flags::real))
+ throw do_taylor(); // Re(x) != 0
+ if ((I*x_pt).info(info_flags::real) && abs(I*x_pt)<_ex1())
+ throw do_taylor(); // Re(x) == 0, but abs(x)<1
+ // if we got here we have to care for cuts and poles
+ return (log((1+I*x)/(1-I*x))/(2*I)).series(rel, order, options);
+}
+
REGISTER_FUNCTION(atan, eval_func(atan_eval).
evalf_func(atan_evalf).
- derivative_func(atan_deriv));
+ derivative_func(atan_deriv).
+ series_func(atan_series));
//////////
// inverse tangent (atan2(y,x))
int order,
unsigned options)
{
+ GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol));
// method:
// Taylor series where there is no pole falls back to tanh_deriv.
// On a pole simply expand sinh(x)/cosh(x).
if (!(2*I*x_pt/Pi).info(info_flags::odd))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole
- return (sinh(x)/cosh(x)).series(rel, order+2);
+ return (sinh(x)/cosh(x)).series(rel, order+2, options);
}
REGISTER_FUNCTION(tanh, eval_func(tanh_eval).
return power(_ex1()-power(x,_ex2()),_ex_1());
}
+static ex atanh_series(const ex &x,
+ const relational &rel,
+ int order,
+ unsigned options)
+{
+ GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol));
+ // method:
+ // Taylor series where there is no pole or cut falls back to atan_deriv.
+ // There are two branch cuts, one runnig from 1 up the real axis and one
+ // one running from -1 down the real axis. The points 1 and -1 are poles
+ // On the branch cuts and the poles series expand
+ // log((1+x)/(1-x))/(2*I)
+ // instead.
+ // (The constant term on the cut itself could be made simpler.)
+ const ex x_pt = x.subs(rel);
+ if (!(x_pt).info(info_flags::real))
+ throw do_taylor(); // Im(x) != 0
+ if ((x_pt).info(info_flags::real) && abs(x_pt)<_ex1())
+ throw do_taylor(); // Im(x) == 0, but abs(x)<1
+ // if we got here we have to care for cuts and poles
+ return (log((1+x)/(1-x))/2).series(rel, order, options);
+}
+
REGISTER_FUNCTION(atanh, eval_func(atanh_eval).
evalf_func(atanh_evalf).
- derivative_func(atanh_deriv));
+ derivative_func(atanh_deriv).
+ series_func(atanh_series));
+
#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC