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.

STransform : Distribution(R) -> UPSR

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

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.

distributionBySTransform : UPSR -> Distribution(R)

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