LiouvillianFunction(R, F)

liouv.spad line 1 [edit on github]

• R : Join(Comparable, IntegralDomain)
• F : Join(FunctionSpace(R), RadicalCategory, TranscendentalFunctionCategory)

This package provides liouvillian functions over an integral domain.

Chi : F -> F

Chi(f) denotes the hyperbolic cosine integral

Ci : F -> F

Ci(f) denotes the cosine integral

Ei : F -> F

Ei(f) denotes the exponential integral

Shi : F -> F

Shi(f) denotes the hyperbolic sine integral

Si : F -> F

Si(f) denotes the sine integral

belong? : BasicOperator -> Boolean

belong?(op) checks if op is Liouvillian

dilog : F -> F

dilog(f) denotes the dilogarithm

erf : F -> F

erf(f) denotes the error function

erfi : F -> F

erfi(f) denotes -%i*erf(%i*z)

fresnelC : F -> F

fresnelC(f) denotes the Fresnel integral C

fresnelS : F -> F

fresnelS(f) denotes the Fresnel integral S

integral : (F, SegmentBinding(F)) -> F

integral(f, x = a..b) denotes the definite integral of f with respect to x from a to b.

integral : (F, Symbol) -> F

integral(f, x) indefinite integral of f with respect to x.

li : F -> F

li(f) denotes the logarithmic integral

operator : BasicOperator -> BasicOperator

operator(op) returns the Liouvillian operator based on op