moment_stirling1.h File Reference

Signed Stirling numbers of the first kind. More...

#include <vector>
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"
#include "line/util/population.h"
#include "line/api/moment/moment_stirlingcycle.h"

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Namespaces
namespace	line
namespace	line::moment

Functions
template<class T>
Matrix< T >	line::moment::moment_stirling1 (int n)
	s(i,j) = (-1)^(i-j) sigma(i,j).

Detailed Description

Signed Stirling numbers of the first kind.

Templated port of matlab/src/api/moment/moment_stirling1.m. Every operation is integer or rational, so the exact instantiation returns the transform with no rounding: moment conversions are exactly where double arithmetic hurts, since the alternating binomial sums cancel catastrophically at high order.

Definition in file moment_stirling1.h.