* Knows about integer arguments and that's it. Somebody ought to provide
* some good numerical evaluation some day...
*
- * @exception std::domain_error("lgamma_eval(): logarithmic pole") */
+ * @exception GiNaC::pole_error("lgamma_eval(): logarithmic pole",0) */
static ex lgamma_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
if (x.info(info_flags::posint)) {
return log(factorial(x.exadd(_ex_1())));
} else {
- throw (std::domain_error("lgamma_eval(): logarithmic pole"));
+ throw (pole_error("lgamma_eval(): logarithmic pole",0));
}
}
// lgamma_evalf should be called here once it becomes available
}
-static ex lgamma_series(const ex & x, const relational & rel, int order)
+static ex lgamma_series(const ex & arg,
+ const relational & rel,
+ int order,
+ bool branchcut)
{
// method:
// Taylor series where there is no pole falls back to psi function
// This, however, seems to fail utterly because you run into branch-cut
// problems. Somebody ought to implement it some day using an asymptotic
// series for tgamma:
- const ex x_pt = x.subs(rel);
- if (!x_pt.info(info_flags::integer) || x_pt.info(info_flags::positive))
+ const ex arg_pt = arg.subs(rel);
+ if (!arg_pt.info(info_flags::integer) || arg_pt.info(info_flags::positive))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole of tgamma(-m):
- throw (std::domain_error("lgamma_series: please implemnt my at the poles"));
+ throw (std::overflow_error("lgamma_series: please implement my at the poles"));
return _ex0(); // not reached
}
* arguments, half-integer arguments and that's it. Somebody ought to provide
* some good numerical evaluation some day...
*
- * @exception std::domain_error("tgamma_eval(): simple pole") */
+ * @exception pole_error("tgamma_eval(): simple pole",0) */
static ex tgamma_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
if (x.info(info_flags::posint)) {
return factorial(ex_to_numeric(x).sub(_num1()));
} else {
- throw (std::domain_error("tgamma_eval(): simple pole"));
+ throw (pole_error("tgamma_eval(): simple pole",1));
}
}
// trap half integer arguments:
}
-static ex tgamma_series(const ex & x, const relational & rel, int order)
+static ex tgamma_series(const ex & arg,
+ const relational & rel,
+ int order,
+ bool branchcut)
{
// method:
// Taylor series where there is no pole falls back to psi function
// from which follows
// series(tgamma(x),x==-m,order) ==
// series(tgamma(x+m+1)/(x*(x+1)*...*(x+m)),x==-m,order+1);
- const ex x_pt = x.subs(rel);
- if (!x_pt.info(info_flags::integer) || x_pt.info(info_flags::positive))
+ const ex arg_pt = arg.subs(rel);
+ if (!arg_pt.info(info_flags::integer) || arg_pt.info(info_flags::positive))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole at -m:
- numeric m = -ex_to_numeric(x_pt);
+ numeric m = -ex_to_numeric(arg_pt);
ex ser_denom = _ex1();
for (numeric p; p<=m; ++p)
- ser_denom *= x+p;
- return (tgamma(x+m+_ex1())/ser_denom).series(rel, order+1);
+ ser_denom *= arg+p;
+ return (tgamma(arg+m+_ex1())/ser_denom).series(rel, order+1);
}
if (nx<=-ny)
return pow(_num_1(), ny)*beta(1-x-y, y);
else
- throw (std::domain_error("beta_eval(): simple pole"));
+ throw (pole_error("beta_eval(): simple pole",1));
}
if (ny.is_negative()) {
if (ny<=-nx)
return pow(_num_1(), nx)*beta(1-y-x, x);
else
- throw (std::domain_error("beta_eval(): simple pole"));
+ throw (pole_error("beta_eval(): simple pole",1));
}
return tgamma(x)*tgamma(y)/tgamma(x+y);
}
}
-static ex beta_series(const ex & x, const ex & y, const relational & rel, int order)
+static ex beta_series(const ex & arg1,
+ const ex & arg2,
+ const relational & rel,
+ int order,
+ bool branchcut)
{
// method:
// Taylor series where there is no pole of one of the tgamma functions
// falls back to beta function evaluation. Otherwise, fall back to
// tgamma series directly.
- const ex x_pt = x.subs(rel);
- const ex y_pt = y.subs(rel);
+ const ex arg1_pt = arg1.subs(rel);
+ const ex arg2_pt = arg2.subs(rel);
GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol));
const symbol *s = static_cast<symbol *>(rel.lhs().bp);
- ex x_ser, y_ser, xy_ser;
- if ((!x_pt.info(info_flags::integer) || x_pt.info(info_flags::positive)) &&
- (!y_pt.info(info_flags::integer) || y_pt.info(info_flags::positive)))
+ ex arg1_ser, arg2_ser, arg1arg2_ser;
+ if ((!arg1_pt.info(info_flags::integer) || arg1_pt.info(info_flags::positive)) &&
+ (!arg2_pt.info(info_flags::integer) || arg2_pt.info(info_flags::positive)))
throw do_taylor(); // caught by function::series()
- // trap the case where x is on a pole directly:
- if (x.info(info_flags::integer) && !x.info(info_flags::positive))
- x_ser = tgamma(x+*s).series(rel,order);
+ // trap the case where arg1 is on a pole:
+ if (arg1.info(info_flags::integer) && !arg1.info(info_flags::positive))
+ arg1_ser = tgamma(arg1+*s).series(rel,order);
else
- x_ser = tgamma(x).series(rel,order);
- // trap the case where y is on a pole directly:
- if (y.info(info_flags::integer) && !y.info(info_flags::positive))
- y_ser = tgamma(y+*s).series(rel,order);
+ arg1_ser = tgamma(arg1).series(rel,order);
+ // trap the case where arg2 is on a pole:
+ if (arg2.info(info_flags::integer) && !arg2.info(info_flags::positive))
+ arg2_ser = tgamma(arg2+*s).series(rel,order);
else
- y_ser = tgamma(y).series(rel,order);
- // trap the case where y is on a pole directly:
- if ((x+y).info(info_flags::integer) && !(x+y).info(info_flags::positive))
- xy_ser = tgamma(y+x+*s).series(rel,order);
+ arg2_ser = tgamma(arg2).series(rel,order);
+ // trap the case where arg1+arg2 is on a pole:
+ if ((arg1+arg2).info(info_flags::integer) && !(arg1+arg2).info(info_flags::positive))
+ arg1arg2_ser = tgamma(arg2+arg1+*s).series(rel,order);
else
- xy_ser = tgamma(y+x).series(rel,order);
- // compose the result:
- return (x_ser*y_ser/xy_ser).series(rel,order);
+ arg1arg2_ser = tgamma(arg2+arg1).series(rel,order);
+ // compose the result (expanding all the terms):
+ return (arg1_ser*arg2_ser/arg1arg2_ser).series(rel,order).expand();
}
return rat-Euler;
} else {
// for non-positive integers there is a pole:
- throw (std::domain_error("psi_eval(): simple pole"));
+ throw (pole_error("psi_eval(): simple pole",1));
}
}
if ((_num2()*nx).is_integer()) {
return psi(_ex1(), x);
}
-static ex psi1_series(const ex & x, const relational & rel, int order)
+static ex psi1_series(const ex & arg,
+ const relational & rel,
+ int order,
+ bool branchcut)
{
// method:
// Taylor series where there is no pole falls back to polygamma function
// from which follows
// series(psi(x),x==-m,order) ==
// series(psi(x+m+1) - 1/x - 1/(x+1) - 1/(x+m)),x==-m,order);
- const ex x_pt = x.subs(rel);
- if (!x_pt.info(info_flags::integer) || x_pt.info(info_flags::positive))
+ const ex arg_pt = arg.subs(rel);
+ if (!arg_pt.info(info_flags::integer) || arg_pt.info(info_flags::positive))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole at -m:
- numeric m = -ex_to_numeric(x_pt);
+ numeric m = -ex_to_numeric(arg_pt);
ex recur;
for (numeric p; p<=m; ++p)
- recur += power(x+p,_ex_1());
- return (psi(x+m+_ex1())-recur).series(rel, order);
+ recur += power(arg+p,_ex_1());
+ return (psi(arg+m+_ex1())-recur).series(rel, order);
}
const unsigned function_index_psi1 =
return recur+psi(n,_ex1());
} else {
// for non-positive integers there is a pole:
- throw (std::domain_error("psi2_eval(): pole"));
+ throw (pole_error("psi2_eval(): pole",1));
}
}
if ((_num2()*nx).is_integer()) {
return psi(n+_ex1(), x);
}
-static ex psi2_series(const ex & n, const ex & x, const relational & rel, int order)
+static ex psi2_series(const ex & n,
+ const ex & arg,
+ const relational & rel,
+ int order,
+ bool branchcut)
{
// method:
// Taylor series where there is no pole falls back to polygamma function
// series(psi(x),x==-m,order) ==
// series(psi(x+m+1) - (-1)^n * n! * ((x)^(-n-1) + (x+1)^(-n-1) + ...
// ... + (x+m)^(-n-1))),x==-m,order);
- const ex x_pt = x.subs(rel);
- if (!x_pt.info(info_flags::integer) || x_pt.info(info_flags::positive))
+ const ex arg_pt = arg.subs(rel);
+ if (!arg_pt.info(info_flags::integer) || arg_pt.info(info_flags::positive))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a pole of order n+1 at -m:
- numeric m = -ex_to_numeric(x_pt);
+ numeric m = -ex_to_numeric(arg_pt);
ex recur;
for (numeric p; p<=m; ++p)
- recur += power(x+p,-n+_ex_1());
+ recur += power(arg+p,-n+_ex_1());
recur *= factorial(n)*power(_ex_1(),n);
- return (psi(n, x+m+_ex1())-recur).series(rel, order);
+ return (psi(n, arg+m+_ex1())-recur).series(rel, order);
}
const unsigned function_index_psi2 =
git://www.ginac.de / ginac.git / blobdiff