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 ArcSin

 http://functions.wolfram.com/01.12.21.0014.01

 Input Form

 Integrate[ArcSin[z Sin[t]], {t, 0, Pi/2}] == (1/4) z LerchPhi[z^2, 2, 1/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", FractionBox["\[Pi]", "2"]], RowBox[List[RowBox[List["ArcSin", "[", RowBox[List["z", " ", RowBox[List["Sin", "[", "t", "]"]]]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "4"], " ", "z", " ", RowBox[List["LerchPhi", "[", RowBox[List[SuperscriptBox["z", "2"], ",", "2", ",", FractionBox["1", "2"]]], "]"]]]]]]]]

 MathML Form

 0 π 2 sin - 1 ( z sin ( t ) ) t 1 4 z Φ ( z 2 , 2 , 1 2 ) TagBox[RowBox[List["\[CapitalPhi]", "(", RowBox[List[TagBox[SuperscriptBox["z", "2"], Rule[Editable, True]], ",", TagBox["2", Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[\$CellContext`e1, \$CellContext`e2, \$CellContext`e3], LerchPhi[\$CellContext`e1, \$CellContext`e2, \$CellContext`e3]]]] t 0 2 -1 z t 1 4 z LerchPhi z 2 2 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", FractionBox["\[Pi]", "2"]], RowBox[List[RowBox[List["ArcSin", "[", RowBox[List["z_", " ", RowBox[List["Sin", "[", "t_", "]"]]]], "]"]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", "z", " ", RowBox[List["LerchPhi", "[", RowBox[List[SuperscriptBox["z", "2"], ",", "2", ",", FractionBox["1", "2"]]], "]"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29