See also
Caution! There is no guarantee for the following information. They are obtained by guessing. In the future, the company may change them in an incompatible way.
System`
-
DuplicateFreeQ[list](>= v9.0)
DuplicateFreeQ[{1, 2, 3}] // Print; (* True*)
DuplicateFreeQ[{1, 2, 1}] // Print; (* False *)
TensorQ[expr]Optional arguments of
Return[expr, func]andBreak[func]
(http://mathematica.stackexchange.com/a/6757)
f[x_] := Module[{},
Do[If[x > 5, Return[a]], {3}]; x
];
f[6] // Print; (* 6 *)
f[x_] := Module[{},
Do[If[x > 5, Return[a, Module]], {3}]; x
];
f[6] // Print; (* a *)
System`Private`
-
InternalSeries[f, {x, x0, n}](>= v5.1)
Func /: System`Private`InternalSeries[Func[x_], {x_, 0, n_Integer}] :=
Sum[x^i, {i, 0, n}] + x^n * O[x];
Series[Func[x] / x, {x, 0, 2}] // Print; (* 1/x + 1 + x + x^2 + O[x]^3 *)
SpecialFunctions`
Give the following a try:
?SpecialFunctions`*
-
HarmonicPolyLog[{m1, ..., mk}, x](>= v9.0) -
FunctionExpandHarmonicPolyLog[expr](>= v9.0) -
MultipleFiniteHarmonicSumS[{m1, ..., mk}, n](>= v9.0) -
MultiplePolyLog[{m1, ..., mk}, {z1, ..., zk}](>= v9.0) -
MultipleZetaValue[{m1, ..., mk}](>= v9.0) -
ShuffleProductExpand[expr](>= v9.0) -
StuffleProductExpand[expr](>= v9.0)
It seems that the definitions of harmonic polylogarithms and multipolylogarithms are the same as Remiddi and Vermaseren and Vollinga and Weinzierl, respectively:
(* HPL 2.0, Mathematica 10.1.0 *)
<<HPL`;
HPL[{1, -2, 3, 0}, 0.7] // Print;
SpecialFunctions`HarmonicPolyLog[{1, -2, 3, 0}, 0.7] // Print;
SpecialFunctions`MultiplePolyLog[{1, -2, 3, 0}, {0.7, 1, 1, 1}] // Print;
-0.25112
-0.25112
-0.25112
Still the implementation is mysterious...
(* Mathematica 10.1.0 *)
Series[PolyLog[2, 1 - x], {x, 0, 1}] // Print;
Series[SpecialFunctions`HarmonicPolyLog[{2}, 1 - x] // FunctionExpand, {x, 0, 1}] // Print;
Series[SpecialFunctions`HarmonicPolyLog[{2}, 1 - x], {x, 0, 1}, Assumptions -> 0 < x < 1] // Print;
Pi^2/6 + (-1+Log[x]) x + O[x]^2
Pi^2/6 + (-1+Log[x]) x + O[x]^2
Pi^2/6 + (-1-2*I*Pi+Log[x]) x + O[x]^2
Less known functions
Only usage messages by ?Command are available.
ArgumentCountQ[head, len, min, max]-
ArgumentCountQ[head, len, {m1, m2, ..., mi}](>= v8.0)
TwoArgFunc[a___] := Null /; ArgumentCountQ[TwoArgFunc, Length[{a}], 2, 2] && False;
TwoArgFunc[1, 2] // Print; (* TwoArgFunc[1, 2] *)
TwoArgFunc[1, 2, 3] // Print; (* TwoArgFunc[1, 2, 3] with an error message "TwoArgFunc::argrx: TwoArgFunc called with 3 arguments; 2 arguments are expected." *)
ListQ[expr]OptionQ[e]
In >= v6.0, one can use OptionsPattern and OptionValue for manipulating options.
StringQ[expr]