moment_stirlingcycle.h File Reference

Unsigned Stirling numbers of the first kind (cycle numbers), orders 0..n. More...

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

Include dependency graph for moment_stirlingcycle.h:

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Namespaces
namespace	line
namespace	line::moment

Functions
template<class T>
Matrix< T >	line::moment::moment_stirlingcycle (int n)
	sigma(i,j), (n+1) x (n+1) lower triangular, sigma(0,0) = 1.

Detailed Description

Unsigned Stirling numbers of the first kind (cycle numbers), orders 0..n.

Templated port of matlab/src/api/moment/moment_stirlingcycle.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_stirlingcycle.h.