moment_stirling2.h File Reference

Stirling numbers of the second kind. More...

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

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Namespaces
namespace	line
namespace	line::moment

Functions
template<class T>
Matrix< T >	line::moment::moment_stirling2 (int n)
	S(i,j) = j S(i-1,j) + S(i-1,j-1), S(0,0) = 1.

Detailed Description

Stirling numbers of the second kind.

Templated port of matlab/src/api/moment/moment_stirling2.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_stirling2.h.