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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1},{b1,b2},z] > Specific values > For rational parameters with larger denominators and fixed z > For fixed z and a1=15/4, b1`>=-11/2 > For fixed z and a1=15/4, b1`=1/2





http://functions.wolfram.com/07.22.03.aetx.01









  


  








Input Form





HypergeometricPFQ[{15/4}, {1/2, 21/4}, -z] == (1/(2523136 Sqrt[2] z^(15/4))) (3315 (2 Sqrt[z] (405405 + 376992 z - 96768 z^2 + 8192 z^3) BesselJ[1/4, Sqrt[z]]^2 - 3 (675675 + 1108800 z - 437248 z^2 + 49152 z^3) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (2027025 - 997920 z + 158208 z^2 - 8192 z^3) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", FractionBox["15", "4"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["21", "4"]]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["3315", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["405405", "+", RowBox[List["376992", " ", "z"]], "-", RowBox[List["96768", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8192", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselJ", "[", RowBox[List[FractionBox["1", "4"], ",", SqrtBox["z"]]], "]"]], "2"]]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List["675675", "+", RowBox[List["1108800", " ", "z"]], "-", RowBox[List["437248", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["49152", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["BesselJ", "[", RowBox[List[FractionBox["1", "4"], ",", SqrtBox["z"]]], "]"]], " ", RowBox[List["BesselJ", "[", RowBox[List[FractionBox["5", "4"], ",", SqrtBox["z"]]], "]"]]]], "+", RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["2027025", "-", RowBox[List["997920", " ", "z"]], "+", RowBox[List["158208", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["8192", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselJ", "[", RowBox[List[FractionBox["5", "4"], ",", SqrtBox["z"]]], "]"]], "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["5", "4"], "]"]], "2"]]], RowBox[List["2523136", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["15", "/", "4"]]]]]]]]]]


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





2007-05-02