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 | | http://functions.wolfram.com/07.22.03.aag3.01 | 
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 | | HypergeometricPFQ[{-(5/4)}, {5/2, 1/4}, -z] == 
 (1/(77 z^(1/4))) (Sqrt[2] ((77 + 304 z + 128 z^2) BesselJ[1/4, Sqrt[z]]^2 - 
    96 Sqrt[z] (3 + 2 z) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 
    (-25 + 208 z + 128 z^2) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["-", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", FractionBox["1", "4"]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["77", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], RowBox[List["(", RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["77", "+", RowBox[List["304", " ", "z"]], "+", RowBox[List["128", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselJ", "[", RowBox[List[FractionBox["1", "4"], ",", SqrtBox["z"]]], "]"]], "2"]]], "-", RowBox[List["96", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "z"]]]], ")"]], " ", RowBox[List["BesselJ", "[", RowBox[List[FractionBox["1", "4"], ",", SqrtBox["z"]]], "]"]], " ", RowBox[List["BesselJ", "[", RowBox[List[FractionBox["5", "4"], ",", SqrtBox["z"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "25"]], "+", RowBox[List["208", " ", "z"]], "+", RowBox[List["128", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselJ", "[", RowBox[List[FractionBox["5", "4"], ",", SqrtBox["z"]]], "]"]], "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["5", "4"], "]"]], "2"]]], ")"]]]]]]]] | 
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   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 1 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 5 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mfrac>  <mn> 5 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 1 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "1"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["5", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation>  </semantics>  <mo>  </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 77 </mn>  <mo> ⁢ </mo>  <mroot>  <mi> z </mi>  <mn> 4 </mn>  </mroot>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <msqrt>  <mn> 2 </mn>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 128 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 304 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 77 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mrow>  <msub>  <mi> J </mi>  <mfrac>  <mn> 1 </mn>  <mn> 4 </mn>  </mfrac>  </msub>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 96 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 3 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msub>  <mi> J </mi>  <mfrac>  <mn> 5 </mn>  <mn> 4 </mn>  </mfrac>  </msub>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msub>  <mi> J </mi>  <mfrac>  <mn> 1 </mn>  <mn> 4 </mn>  </mfrac>  </msub>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 128 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 208 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 25 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mrow>  <msub>  <mi> J </mi>  <mfrac>  <mn> 5 </mn>  <mn> 4 </mn>  </mfrac>  </msub>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mn> 5 </mn>  <mn> 4 </mn>  </mfrac>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 5 <sep /> 4 </cn>  </apply>  </list>  <list>  <cn type='rational'> 5 <sep /> 2 </cn>  <cn type='rational'> 1 <sep /> 4 </cn>  </list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 77 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 128 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 304 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 77 </cn>  </apply>  <apply>  <power />  <apply>  <ci> BesselJ </ci>  <cn type='rational'> 1 <sep /> 4 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 96 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 3 </cn>  </apply>  <apply>  <ci> BesselJ </ci>  <cn type='rational'> 5 <sep /> 4 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <ci> BesselJ </ci>  <cn type='rational'> 1 <sep /> 4 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 128 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 208 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -25 </cn>  </apply>  <apply>  <power />  <apply>  <ci> BesselJ </ci>  <cn type='rational'> 5 <sep /> 4 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <ci> Gamma </ci>  <cn type='rational'> 5 <sep /> 4 </cn>  </apply>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["-", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", FractionBox["1", "4"]]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["77", "+", RowBox[List["304", " ", "z"]], "+", RowBox[List["128", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselJ", "[", RowBox[List[FractionBox["1", "4"], ",", SqrtBox["z"]]], "]"]], "2"]]], "-", RowBox[List["96", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "z"]]]], ")"]], " ", RowBox[List["BesselJ", "[", RowBox[List[FractionBox["1", "4"], ",", SqrtBox["z"]]], "]"]], " ", RowBox[List["BesselJ", "[", RowBox[List[FractionBox["5", "4"], ",", SqrtBox["z"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "25"]], "+", RowBox[List["208", " ", "z"]], "+", RowBox[List["128", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselJ", "[", RowBox[List[FractionBox["5", "4"], ",", SqrtBox["z"]]], "]"]], "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["5", "4"], "]"]], "2"]]], RowBox[List["77", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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 | | HypergeometricPFQ[{},{},z] |  | HypergeometricPFQ[{},{b},z] |  | HypergeometricPFQ[{a},{},z] |  | HypergeometricPFQ[{a},{b},z] |  | HypergeometricPFQ[{a1,a2},{b1},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] |  | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] |  | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] |  |  | 
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