Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0641)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=9/2

http://functions.wolfram.com/07.22.03.0641.01

Input Form

HypergeometricPFQ[{-(11/2)}, {9/2, 11/2}, z] == (1/(108716359680 z^(9/2))) (-2 Sqrt[z] (6188663250 + 17604712125 z + 15173217675 z^2 + 12818906100 z^3 - 9408005010 z^4 + 1080169470 z^5 - 41597730 z^6 + 639552 z^7 - 3956 z^8 + 8 z^9) Cosh[2 Sqrt[z]] - (-6188663250 + 9507526875 z + 11491828425 z^2 + 7368391800 z^3 - 8520677550 z^4 + 1041848730 z^5 - 40979430 z^6 + 635640 z^7 - 3948 z^8 + 8 z^9) Sinh[2 Sqrt[z]] + 16 z (2210236875 + 3978426375 z + 3536379000 z^2 + 4125775500 z^3 - 2475465300 z^4 + 275051700 z^5 - 10478160 z^6 + 160380 z^7 - 990 z^8 + 2 z^9) SinhIntegral[2 Sqrt[z]])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["-", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["9", "2"], ",", FractionBox["11", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["108716359680", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["6188663250", "+", RowBox[List["17604712125", " ", "z"]], "+", RowBox[List["15173217675", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["12818906100", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["9408005010", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1080169470", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["41597730", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["639552", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["3956", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["8", " ", SuperscriptBox["z", "9"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", SqrtBox["z"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "6188663250"]], "+", RowBox[List["9507526875", " ", "z"]], "+", RowBox[List["11491828425", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7368391800", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["8520677550", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1041848730", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["40979430", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["635640", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["3948", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["8", " ", SuperscriptBox["z", "9"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", SqrtBox["z"]]], "]"]]]], "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List["2210236875", "+", RowBox[List["3978426375", " ", "z"]], "+", RowBox[List["3536379000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4125775500", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2475465300", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["275051700", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["10478160", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["160380", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["990", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["2", " ", SuperscriptBox["z", "9"]]]]], ")"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["2", " ", 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> 1 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 11 </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]", "1"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["11", "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["9", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "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> <mn> 1 </mn> <mrow> <mn> 108716359680 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3956 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 639552 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 41597730 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1080169470 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 9408005010 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12818906100 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 15173217675 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 17604712125 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 6188663250 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3948 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 635640 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 40979430 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1041848730 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8520677550 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7368391800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11491828425 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9507526875 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 6188663250 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 990 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 160380 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10478160 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 275051700 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2475465300 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4125775500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3536379000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3978426375 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2210236875 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Shi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </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'> 11 <sep /> 2 </cn> </apply> </list> <list> <cn type='rational'> 9 <sep /> 2 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 108716359680 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3956 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 639552 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 41597730 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1080169470 </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'> 9408005010 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 12818906100 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 15173217675 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17604712125 </cn> <ci> z </ci> </apply> <cn type='integer'> 6188663250 </cn> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3948 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 635640 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40979430 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1041848730 </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'> 8520677550 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7368391800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11491828425 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9507526875 </cn> <ci> z </ci> </apply> <cn type='integer'> -6188663250 </cn> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 990 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 160380 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10478160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 275051700 </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'> 2475465300 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4125775500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3536379000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3978426375 </cn> <ci> z </ci> </apply> <cn type='integer'> 2210236875 </cn> </apply> <apply> <ci> SinhIntegral </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </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["-", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["9", "2"], ",", FractionBox["11", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["6188663250", "+", RowBox[List["17604712125", " ", "z"]], "+", RowBox[List["15173217675", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["12818906100", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["9408005010", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1080169470", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["41597730", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["639552", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["3956", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["8", " ", SuperscriptBox["z", "9"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", SqrtBox["z"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "6188663250"]], "+", RowBox[List["9507526875", " ", "z"]], "+", RowBox[List["11491828425", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7368391800", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["8520677550", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1041848730", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["40979430", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["635640", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["3948", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["8", " ", SuperscriptBox["z", "9"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", SqrtBox["z"]]], "]"]]]], "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List["2210236875", "+", RowBox[List["3978426375", " ", "z"]], "+", RowBox[List["3536379000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4125775500", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2475465300", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["275051700", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["10478160", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["160380", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["990", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["2", " ", SuperscriptBox["z", "9"]]]]], ")"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["2", " ", SqrtBox["z"]]], "]"]]]]]], RowBox[List["108716359680", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]]

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,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,...,a_p},{b₁,...,b_q},z]