STransformPackage(R, UTSR, ULSR, UPSR)

distro.spad line 513 [edit on github]

• R: Join(CommutativeRing, Algebra Fraction Integer)

• UTSR: UnivariateTaylorSeriesCategory R

• ULSR: UnivariateLaurentSeriesConstructorCategory(R, UTSR)

• UPSR: UnivariatePuiseuxSeriesConstructorCategory(R, ULSR)

A package to compute Taylor and Puiseux series of S-transforms.

distributionBySTransform: UPSR -> Distribution R

distributionBySTransform(x) returns the distribution with S-transform x.

STransform1: Distribution R -> UTSR

STransform(x) returns the Taylor expansion of the S-transform S(z) of the distribution x if the mean is nonzero.

STransform2: Distribution R -> UPSR

STransform(x) returns the Puiseux expansion of the S-transform S(z) if the mean is zero.

STransform: Distribution R -> UPSR

STransform(x) returns the Puiseux expansion of the S-transform S(z).