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Cosh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.20.26.0078.01









  


  










Input Form





Cosh[a + z] Hypergeometric0F1[b, z^2/4] == ((2^(-3 + 2 b) Gamma[b])/Sqrt[Pi]) (MeijerG[{{3/2 - b}, {}}, {{0}, {2 - 2 b}}, 2 z]/E^a + E^a Pi Csc[b Pi] MeijerG[{{3/2 - b}, {1 - b}}, {{0}, {2 - 2 b, 1 - b}}, 2 z])










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["Cosh", "[", RowBox[List["a_", "+", "z_"]], "]"]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List["b_", ",", FractionBox[SuperscriptBox["z_", "2"], "4"]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "b"]]]]], " ", RowBox[List["Gamma", "[", "b", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "a"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], "-", "b"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["2", "-", RowBox[List["2", " ", "b"]]]], "}"]]]], "}"]], ",", RowBox[List["2", " ", "z"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "a"], " ", "\[Pi]", " ", RowBox[List["Csc", "[", RowBox[List["b", " ", "\[Pi]"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], "-", "b"]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", "b"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", RowBox[List["2", " ", "b"]]]], ",", RowBox[List["1", "-", "b"]]]], "}"]]]], "}"]], ",", RowBox[List["2", " ", "z"]]]], "]"]]]]]], ")"]]]], SqrtBox["\[Pi]"]]]]]]










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





2003-08-21





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