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| 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=1/2, a2>=1/2  For fixed z and a1=1/2, a2=1, a3>=1  For fixed z and a1=1/2, a2=1, a3=5/2  For fixed z and a1=1/2, a2=1, a3=5/2, b1=3/2   |  |  
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 | | http://functions.wolfram.com/07.27.03.an6s.01 | 
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 | | HypergeometricPFQ[{1/2, 1, 5/2}, {3/2, 7/2}, -z] == 
 -((5 (-3 + z))/(12 z^2)) + (5 (-1 + z^2) ArcTan[Sqrt[z]])/(4 z^(5/2)) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", FractionBox["5", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "z"]], ")"]]]], RowBox[List["12", " ", SuperscriptBox["z", "2"]]]]]], "+", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]], RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["5", "/", "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> 3 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mn> 1 </mn>  <mo> , </mo>  <mfrac>  <mn> 5 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 7 </mn>  <mn> 2 </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]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "2"], 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["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], 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>  <mrow>  <mn> 5 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> tan </mi>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> - </mo>  <mfrac>  <mrow>  <mn> 5 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 3 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 12 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  </mfrac>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='rational'> 1 <sep /> 2 </cn>  <cn type='integer'> 1 </cn>  <cn type='rational'> 5 <sep /> 2 </cn>  </list>  <list>  <cn type='rational'> 3 <sep /> 2 </cn>  <cn type='rational'> 7 <sep /> 2 </cn>  </list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 5 </cn>  <apply>  <plus />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <arctan />  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 4 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 5 </cn>  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> -3 </cn>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 12 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </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["1", "2"], ",", "1", ",", FractionBox["5", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "z"]], ")"]]]], RowBox[List["12", " ", SuperscriptBox["z", "2"]]]]]], "+", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]], RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]]]]]] | 
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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},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2,b3},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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