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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Representations through more general functions > Through Meijer G > Classical cases involving exp and Laguerre L





http://functions.wolfram.com/01.19.26.0118.01









  


  








Input Form





(Sinh[z] LaguerreL[\[Nu], \[Lambda], 2 z])/E^z == (Gamma[\[Nu] + \[Lambda] + 1]/2) MeijerG[{{}, {\[Nu] + 1}}, {{0}, {-\[Lambda]}}, 2 z] - (1/(2 Gamma[\[Nu] + 1])) MeijerG[{{-\[Nu] - \[Lambda]}, {}}, {{0}, {-\[Lambda]}}, 2 z]








Standard Form





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MathML Form







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</ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </list> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#955; </ci> </apply> </list> </list> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z_"]]], " ", RowBox[List["Sinh", "[", "z_", "]"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]_", ",", "\[Lambda]_", ",", RowBox[List["2", " ", "z_"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "\[Lambda]", "+", "1"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["\[Nu]", "+", "1"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["-", "\[Lambda]"]], "}"]]]], "}"]], ",", RowBox[List["2", " ", "z"]]]], "]"]]]], "-", FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "\[Lambda]"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["-", "\[Lambda]"]], "}"]]]], "}"]], ",", RowBox[List["2", " ", "z"]]]], "]"]], RowBox[List["2", " ", RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]]]]]]]]]]]


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





2007-05-02