Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.5169)

HypergeometricPFQ

$Mathematica Notation$

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-1/2, a₃>=-1/2

For fixed z and a₁=-7/2, a₂=-1/2, a₃=2

For fixed z and a₁=-7/2, a₂=-1/2, a₃=2, b₁=3/2

http://functions.wolfram.com/07.27.03.5169.01

Input Form

HypergeometricPFQ[{-(7/2), -(1/2), 2}, {3/2, 7/2}, z] == (-210 + 1190 z + 63507 z^2 + 14833 z^3 - 2835 z^4 + 315 z^5)/(98304 z^2) + (35 (-2 + 12 z - 215 z^2 + 80 z^3 + 150 z^4 - 28 z^5 + 3 z^6) Log[1 - Sqrt[z]])/(65536 z^(5/2)) - (35 (-2 + 12 z - 215 z^2 + 80 z^3 + 150 z^4 - 28 z^5 + 3 z^6) Log[1 + Sqrt[z]])/(65536 z^(5/2)) - (525 (1 + 4 z) PolyLog[2, -Sqrt[z]])/ (8192 Sqrt[z]) + (525 (1 + 4 z) PolyLog[2, Sqrt[z]])/(8192 Sqrt[z])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "210"]], "+", RowBox[List["1190", " ", "z"]], "+", RowBox[List["63507", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["14833", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2835", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["315", " ", SuperscriptBox["z", "5"]]]]], RowBox[List["98304", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["12", " ", "z"]], "-", RowBox[List["215", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["80", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["150", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["28", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["3", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"]]], "]"]]]], RowBox[List["65536", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["12", " ", "z"]], "-", RowBox[List["215", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["80", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["150", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["28", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["3", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"]]], "]"]]]], RowBox[List["65536", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["525", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]], RowBox[List["8192", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["525", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["8192", " ", SqrtBox["z"]]]]]]]]]]

MathML Form

<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> <mrow> <mo> - </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 2 </mn> </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> <mi> z </mi> </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[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["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["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> <mrow> <mn> 315 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2835 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 14833 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 63507 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1190 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 210 </mn> </mrow> <mrow> <mn> 98304 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 35 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 28 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 150 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 80 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 215 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 65536 </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> 35 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 28 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 150 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 80 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 215 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 65536 </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> 525 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 8192 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 525 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 8192 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 2 </cn> </list> <list> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 315 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2835 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 14833 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 63507 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1190 </cn> <ci> z </ci> </apply> <cn type='integer'> -210 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 98304 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 28 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 150 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 80 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 215 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> <cn type='integer'> -2 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 65536 </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'> 35 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 28 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 150 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 80 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 215 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> <cn type='integer'> -2 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 65536 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 525 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8192 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 525 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8192 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "210"]], "+", RowBox[List["1190", " ", "z"]], "+", RowBox[List["63507", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["14833", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2835", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["315", " ", SuperscriptBox["z", "5"]]]]], RowBox[List["98304", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["12", " ", "z"]], "-", RowBox[List["215", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["80", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["150", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["28", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["3", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"]]], "]"]]]], RowBox[List["65536", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["12", " ", "z"]], "-", RowBox[List["215", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["80", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["150", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["28", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["3", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"]]], "]"]]]], RowBox[List["65536", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["525", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]], RowBox[List["8192", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["525", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["8192", " ", SqrtBox["z"]]]]]]]]]]

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

2007-05-02

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,...,a_p},{b₁,...,b_q},z]