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variants of this functions
Hypergeometric0F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric0F1Regularized[b,z] > Representations through more general functions > Through Meijer G > Classical cases involving cos





http://functions.wolfram.com/07.18.26.0015.01









  


  








Input Form





Cos[a + 2 Sqrt[z]] Hypergeometric0F1Regularized[b, -z] == 2^(-(3/2) + b) MeijerG[{{(1/4) (3 - 2 b), (1/4) (5 - 2 b)}, {1/2 + a/Pi}}, {{0, 1/2}, {1 - b, 3/2 - b, 1/2 + a/Pi}}, 4 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["Cos", "[", RowBox[List["a_", "+", RowBox[List["2", " ", SqrtBox["z_"]]]]], "]"]], " ", RowBox[List["Hypergeometric0F1Regularized", "[", RowBox[List["b_", ",", RowBox[List["-", "z_"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], "+", "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["{", RowBox[List[FractionBox["1", "2"], "+", FractionBox["a", "\[Pi]"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "b"]], ",", RowBox[List[FractionBox["3", "2"], "-", "b"]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["a", "\[Pi]"]]]]], "}"]]]], "}"]], ",", RowBox[List["4", " ", "z"]]]], "]"]]]]]]]]


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





2001-10-29