EllipticFunctionsUnivariateTaylorSeries(Coef, UTS)

elfuts.spad line 1 [edit on github]

• Coef : Field
• UTS : UnivariateTaylorSeriesCategory(Coef)

The elliptic functions sn, sc and dn are expanded as Taylor series.

ellipticE : (UTS, Coef) -> UTS

ellipticE(z, m) expands the elliptic integral E as a Taylor series in z.

ellipticF : (UTS, Coef) -> UTS

ellipticF(z, m) expands the elliptic integral F as a Taylor series in z.

ellipticPi : (UTS, Coef, Coef) -> UTS

ellipticPi(z, n, m) expands the elliptic integral Pi as a Taylor series in z.

jacobiCn : (UTS, Coef) -> UTS

jacobiCn(z, m) expands the elliptic function cn as a Taylor series in z.

jacobiDn : (UTS, Coef) -> UTS

jacobiDn(z, m) expands the elliptic function dn as a Taylor series in z.

jacobiSn : (UTS, Coef) -> UTS

jacobiSn(z, m) expands the elliptic function sn as a Taylor series in z.

sncndn : (Stream(Coef), Coef) -> List(Stream(Coef))

sncndn(s, c) is used internally.