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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Representations through more general functions > Through Meijer G > Classical cases involving 0F1





http://functions.wolfram.com/01.19.26.0025.01









  


  








Input Form





Sinh[z] Hypergeometric0F1[b, z^2/4] == (-2^(-(3/2) + b)) Pi Csc[(b Pi)/2] Gamma[b] MeijerG[{{(1/4) (3 - 2 b), (1/4) (5 - 2 b)}, {(1/2) (1 - b)}}, {{1/2}, {0, (1/2) (1 - b), 1 - b, 3/2 - b}}, z^2] /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/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["Sinh", "[", "z_", "]"]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List["b_", ",", FractionBox[SuperscriptBox["z_", "2"], "4"]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], "+", "b"]]]]], " ", "\[Pi]", " ", RowBox[List["Csc", "[", FractionBox[RowBox[List["b", " ", "\[Pi]"]], "2"], "]"]], " ", RowBox[List["Gamma", "[", "b", "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "b"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "b"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["1", "-", "b"]], "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox[RowBox[List["1", "-", "b"]], "2"], ",", RowBox[List["1", "-", "b"]], ",", RowBox[List[FractionBox["3", "2"], "-", "b"]]]], "}"]]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]


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





2001-10-29