# MomentPackage R¶

An auxiliary package for various moment and cumulant transformations used in Distribution.

booleanCumulant2moment: Sequence R -> Sequence R
booleanCumulant2moment(cc) computes the sequence of moments from the sequence of boolean cumulants cc
cumulant2moment: Sequence R -> Sequence R
cumulant2moment(cc) computes the sequence of moments from the sequence of classical cumulants cc
freeCumulant2moment: Sequence R -> Sequence R
freeCumulant2moment(cc) computes the sequence of moments from the sequence of free cumulants cc
hankelDeterminant: (Sequence R, NonNegativeInteger) -> R
hankelDeterminant(x, n) returns the nth Hankel determinant of the sequence x.
jacobi2poly: (Stream R, Stream R) -> Stream SparseUnivariatePolynomial R
jacobi2poly(aa, bb) returns the stream of orthogonal polynomials corresponding to the Jacobi parameters a_n and b_n.
moment2booleanCumulant: Sequence R -> Sequence R
moment2booleanCumulant(mm) computes the sequence of boolean cumulants from the sequence of moments mm
moment2cumulant: Sequence R -> Sequence R
moment2cumulant(mm) computes the sequence of classical cumulants from the sequence of moments mm
moment2freeCumulant: Sequence R -> Sequence R
moment2freeCumulant(mm) computes the sequence of free cumulants from the sequence of moments mm
moment2jacobi2: Sequence R -> Stream Record(an: R, bn: R) if R has Field
moment2jacobi2(mm) computes the Jacobi parameters as stream of pairs $(an, bn)$.
moment2jacobi: Sequence R -> Record(an: Stream R, bn: Stream R) if R has Field
moment2jacobi(mm) computes the Jacobi parameters as pair of streams.
moment2monotoneCumulant: Sequence R -> Sequence R
moment2monotoneCumulant(mm) computes the sequence of monotone cumulants from the sequence of moments mm
moment2nthJacobi: List R -> Record(an: List R, bn: List R) if R has Field
moment2nthJacobi(mm) computes the list of Jacobi parameters from the list of moments mm as far as possible.
moment2Stransform: Sequence R -> Record(puiseux: Fraction Integer, laurent: Fraction Integer, coef: Sequence R) if R has Algebra Fraction Integer
moment2Stransform(x) returns the Puiseux and Laurent order and coefficients of the S transform of x
monotoneCumulant2moment: Sequence R -> Sequence R
monotoneCumulant2moment(hh) computes the sequence of moments from the sequence of monotone cumulants hh
monotoneCumulant2momentPoly: Sequence R -> Sequence SparseUnivariatePolynomial R
monotoneCumulant2momentPoly(hh) computes the sequence of moment polynomials $m_n(t)$ from the sequence of monotone cumulants hh
qcumulant2nthmoment: (R, Sequence R, NonNegativeInteger) -> R
qcumulant2nthmoment(q, cc, n) computes the nth moment from the sequence of reduced q-cumulants cc