PatternMatchIntegration(R, F)ΒΆ

intpm.spad line 1

PatternMatchIntegration provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the literature.

pmComplexintegrate: (F, Symbol) -> Union(Record(special: F, integrand: F), failed) if R has ConvertibleTo Pattern Integer and R has PatternMatchable Integer and F has LiouvillianFunctionCategory
pmComplexintegrate(f, x) returns either “failed” or [g, h] such that integrate(f, x) = g + integrate(h, x). It only looks for special complex integrals that pmintegrate does not return.
pmintegrate: (F, Symbol) -> Union(Record(special: F, integrand: F), failed) if R has ConvertibleTo Pattern Integer and R has PatternMatchable Integer and F has LiouvillianFunctionCategory
pmintegrate(f, x) returns either “failed” or [g,h] such that integrate(f, x) = g + integrate(h, x).
pmintegrate: (F, Symbol, OrderedCompletion F, OrderedCompletion F) -> Union(F, failed) if F has SpecialFunctionCategory and R has PatternMatchable Integer and R has ConvertibleTo Pattern Integer
pmintegrate(f, x = a..b) returns the integral of f(x)dx from a to b if it can be found by the built-in pattern matching rules.
splitConstant: (F, Symbol) -> Record(const: F, nconst: F)
splitConstant(f, x) returns [c, g] such that f = c * g and c does not involve t.