Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.akbw)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=3, a₂>=3

For fixed z and a₁=3, a₂=9/2, b₁>=-11/2

For fixed z and a₁=3, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.akbw.01

Input Form

HypergeometricPFQ[{3, 9/2}, {-(9/2), -(7/2)}, -z] == (1/10418625) (10418625 - 8930250 z + 11226600 z^2 - 32432400 z^3 + 486486000 z^4 + 23156733600 z^5 - 246171744000 z^6 + 508683732480 z^7 - 413958746880 z^8 + 167673331200 z^9 - 37719705600 z^10 + 4965027840 z^11 - 387731456 z^12 + 17522688 z^13 - 419840 z^14 + 4096 z^15) - (1/10418625) ((1024 Sqrt[Pi] (70761600 z^(11/2) - 391910400 z^(13/2) + 647136000 z^(15/2) - 472348800 z^(17/2) + 180139680 z^(19/2) - 39090240 z^(21/2) + 5029920 z^(23/2) - 387000 z^(25/2) + 17315 z^(27/2) - 412 z^(29/2) + 4 z^(31/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["3", ",", FractionBox["9", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "10418625"], RowBox[List["(", RowBox[List["10418625", "-", RowBox[List["8930250", " ", "z"]], "+", RowBox[List["11226600", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["32432400", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["486486000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["23156733600", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["246171744000", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["508683732480", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["413958746880", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["167673331200", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["37719705600", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["4965027840", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["387731456", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["17522688", " ", SuperscriptBox["z", "13"]]], "-", RowBox[List["419840", " ", SuperscriptBox["z", "14"]]], "+", RowBox[List["4096", " ", SuperscriptBox["z", "15"]]]]], ")"]]]], "-", RowBox[List[FractionBox["1", "10418625"], RowBox[List["(", RowBox[List["1024", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["70761600", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["391910400", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["647136000", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "-", RowBox[List["472348800", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "+", RowBox[List["180139680", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "-", RowBox[List["39090240", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "+", RowBox[List["5029920", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "-", RowBox[List["387000", " ", SuperscriptBox["z", RowBox[List["25", "/", "2"]]]]], "+", RowBox[List["17315", " ", SuperscriptBox["z", RowBox[List["27", "/", "2"]]]]], "-", RowBox[List["412", " ", SuperscriptBox["z", RowBox[List["29", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["31", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erfi", "[", 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> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> </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]", "2"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "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[RowBox[List["-", FractionBox["9", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", 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> <mrow> <mfrac> <mn> 1 </mn> <mn> 10418625 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4096 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 15 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 419840 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 14 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 17522688 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 387731456 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4965027840 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 37719705600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 167673331200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 413958746880 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 508683732480 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 246171744000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 23156733600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 486486000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 32432400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11226600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8930250 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 10418625 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 10418625 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1024 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 31 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 412 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 29 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 17315 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 27 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 387000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5029920 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 23 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 39090240 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 21 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 180139680 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 19 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 472348800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 647136000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 391910400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 70761600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 3 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 10418625 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4096 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 15 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 419840 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 14 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 17522688 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 387731456 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4965027840 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 37719705600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 167673331200 </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'> 413958746880 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 508683732480 </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'> 246171744000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 23156733600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 486486000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 32432400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 11226600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8930250 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 10418625 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 10418625 </cn> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 31 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 412 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 29 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 17315 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 27 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 387000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 25 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5029920 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 23 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 39090240 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 21 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 180139680 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 472348800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 647136000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 391910400 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 70761600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <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["3", ",", FractionBox["9", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]]]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["10418625", "-", RowBox[List["8930250", " ", "z"]], "+", RowBox[List["11226600", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["32432400", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["486486000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["23156733600", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["246171744000", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["508683732480", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["413958746880", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["167673331200", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["37719705600", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["4965027840", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["387731456", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["17522688", " ", SuperscriptBox["z", "13"]]], "-", RowBox[List["419840", " ", SuperscriptBox["z", "14"]]], "+", RowBox[List["4096", " ", SuperscriptBox["z", "15"]]]]], "10418625"], "-", FractionBox[RowBox[List["1024", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["70761600", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["391910400", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["647136000", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "-", RowBox[List["472348800", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "+", RowBox[List["180139680", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "-", RowBox[List["39090240", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "+", RowBox[List["5029920", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "-", RowBox[List["387000", " ", SuperscriptBox["z", RowBox[List["25", "/", "2"]]]]], "+", RowBox[List["17315", " ", SuperscriptBox["z", RowBox[List["27", "/", "2"]]]]], "-", RowBox[List["412", " ", SuperscriptBox["z", RowBox[List["29", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["31", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]], "10418625"]]]]]]]

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,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]