Sine: Representations through more general functions (formula 01.06.26.0100)

Sin

$Mathematica Notation$

Elementary Functions

Sin[z]

Representations through more general functions

Through Meijer G

Generalized cases involving Bessel Y

http://functions.wolfram.com/01.06.26.0100.01

Input Form

Sin[a + z] BesselY[\[Nu], z] == (Cos[Pi \[Nu]]/(Sqrt[2] Pi^2)) MeijerG[{{1/4, 3/4}, {-(a/Pi) - \[Nu]/2}}, {{(1 - \[Nu])/2, -(\[Nu]/2), \[Nu]/2, (1 + \[Nu])/2}, {-(a/Pi) - \[Nu]/2}}, z, 1/2] - (1/Sqrt[2]) MeijerG[{{1/4, 3/4}, {(1/2) (1 + (2 a)/Pi + \[Nu])}}, {{\[Nu]/2, (1 + \[Nu])/2}, {(1 - \[Nu])/2, -(\[Nu]/2), (1/2) (1 + (2 a)/Pi + \[Nu])}}, z, 1/2]

Standard Form

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MathML Form

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Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Sin", "[", RowBox[List["a_", "+", "z_"]], "]"]], " ", RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["a", "\[Pi]"]]], "-", FractionBox["\[Nu]", "2"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], ",", RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", FractionBox["\[Nu]", "2"], ",", FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["a", "\[Pi]"]]], "-", FractionBox["\[Nu]", "2"]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox["\[Pi]", "2"]]]], "-", FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["2", " ", "a"]], "\[Pi]"], "+", "\[Nu]"]], ")"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["\[Nu]", "2"], ",", FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], ",", RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["2", " ", "a"]], "\[Pi]"], "+", "\[Nu]"]], ")"]]]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]], SqrtBox["2"]]]]]]]]

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

2003-08-21