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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=-5/2, a2>=-5/2 > For fixed z and a1=-5/2, a2=1/2, a3>=1/2 > For fixed z and a1=-5/2, a2=1/2, a3=2 > For fixed z and a1=-5/2, a2=1/2, a3=2, b1=1





http://functions.wolfram.com/07.27.03.aalb.01









  


  










Input Form





HypergeometricPFQ[{-(5/2), 1/2, 2}, {1, 4}, -z] == (16 (32 + 102 z - 23 z^2 + 496 z^3 + 261 z^4 + 56 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(3465 Pi z^3) + (16 Sqrt[1 + z] (32 + 102 z - 23 z^2 + 496 z^3 + 261 z^4 + 56 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(3465 Pi z^3) + (32 Sqrt[1 + z] (-16 - 49 z + 450 z^2 + 127 z^3 + 28 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(3465 Pi z^3) - (32 (16 + 53 z + 427 z^2 + 623 z^3 + 289 z^4 + 56 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(3465 Pi z^3)










Standard Form





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MathML Form







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</math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", FractionBox["1", "2"], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "4"]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["16", " ", RowBox[List["(", RowBox[List["32", "+", RowBox[List["102", " ", "z"]], "-", RowBox[List["23", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["496", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["261", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["56", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["3465", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox[RowBox[List["16", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["32", "+", RowBox[List["102", " ", "z"]], "-", RowBox[List["23", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["496", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["261", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["56", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["3465", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox[RowBox[List["32", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16"]], "-", RowBox[List["49", " ", "z"]], "+", RowBox[List["450", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["127", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["28", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["3465", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], "-", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["16", "+", RowBox[List["53", " ", "z"]], "+", RowBox[List["427", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["623", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["289", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["56", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["3465", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]]]]]]]]










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





2007-05-02