Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1790)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=3, b₁=6

http://functions.wolfram.com/07.25.03.1790.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {6, 6}, z] == (1920 (32 - 168 z + 133 z^2))/(29393 z^5) + (1/(26942232382065 z^5)) (1024 E^(z/2) (-54997242300 + 316234143225 z - 350412070680 z^2 + 67050408285 z^3 + 9518886720 z^4 + 30127497120 z^5 - 21727681920 z^6 + 5496703632 z^7 - 675032064 z^8 + 43030272 z^9 - 1357824 z^10 + 16640 z^11) BesselI[0, z/2]) - (1/(26942232382065 z^4)) (512 E^(z/2) (207802450485 - 517710544470 z + 171872217090 z^2 + 38481075360 z^3 + 29847903120 z^4 - 34249358304 z^5 + 9764549088 z^6 - 1267977216 z^7 + 83394816 z^8 - 2682368 z^9 + 33280 z^10) BesselI[1, z/2])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List["6", ",", "6"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["1920", " ", RowBox[List["(", RowBox[List["32", "-", RowBox[List["168", " ", "z"]], "+", RowBox[List["133", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], RowBox[List["29393", " ", SuperscriptBox["z", "5"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["26942232382065", " ", SuperscriptBox["z", "5"]]]], RowBox[List["(", RowBox[List["1024", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "54997242300"]], "+", RowBox[List["316234143225", " ", "z"]], "-", RowBox[List["350412070680", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["67050408285", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["9518886720", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["30127497120", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["21727681920", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["5496703632", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["675032064", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["43030272", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["1357824", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["16640", " ", SuperscriptBox["z", "11"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List["26942232382065", " ", SuperscriptBox["z", "4"]]]], RowBox[List["(", RowBox[List["512", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List["207802450485", "-", RowBox[List["517710544470", " ", "z"]], "+", RowBox[List["171872217090", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["38481075360", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["29847903120", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["34249358304", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["9764549088", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["1267977216", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["83394816", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["2682368", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["33280", " ", SuperscriptBox["z", "10"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]], ")"]]]]]]]]]]

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> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ; </mo> <mrow> <mn> 6 </mn> <mo> , </mo> <mn> 6 </mn> </mrow> <mo> ; </mo> <mi> z </mi> </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[RowBox[List["-", FractionBox["11", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", 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> <mn> 1920 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 133 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 168 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 32 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 29393 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 26942232382065 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1024 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> z </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 16640 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1357824 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 43030272 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 675032064 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5496703632 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 21727681920 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 30127497120 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9518886720 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 67050408285 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 350412070680 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 316234143225 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 54997242300 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 26942232382065 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 512 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> z </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 33280 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2682368 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 83394816 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1267977216 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9764549088 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 34249358304 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 29847903120 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 38481075360 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 171872217090 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 517710544470 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 207802450485 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </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> <cn type='integer'> 3 </cn> </list> <list> <cn type='integer'> 6 </cn> <cn type='integer'> 6 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1920 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 133 </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'> 168 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 32 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 29393 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 26942232382065 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 16640 </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'> 1357824 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 43030272 </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'> 675032064 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5496703632 </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'> 21727681920 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 30127497120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9518886720 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 67050408285 </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'> 350412070680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 316234143225 </cn> <ci> z </ci> </apply> <cn type='integer'> -54997242300 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 26942232382065 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 512 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 33280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2682368 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 83394816 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1267977216 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9764549088 </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'> 34249358304 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 29847903120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 38481075360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 171872217090 </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'> 517710544470 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 207802450485 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </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[RowBox[List["-", FractionBox["11", "2"]]], ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List["6", ",", "6"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["1920", " ", RowBox[List["(", RowBox[List["32", "-", RowBox[List["168", " ", "z"]], "+", RowBox[List["133", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], RowBox[List["29393", " ", SuperscriptBox["z", "5"]]]], "+", FractionBox[RowBox[List["1024", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "54997242300"]], "+", RowBox[List["316234143225", " ", "z"]], "-", RowBox[List["350412070680", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["67050408285", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["9518886720", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["30127497120", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["21727681920", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["5496703632", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["675032064", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["43030272", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["1357824", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["16640", " ", SuperscriptBox["z", "11"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", FractionBox["z", "2"]]], "]"]]]], RowBox[List["26942232382065", " ", SuperscriptBox["z", "5"]]]], "-", FractionBox[RowBox[List["512", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", "/", "2"]]], " ", RowBox[List["(", RowBox[List["207802450485", "-", RowBox[List["517710544470", " ", "z"]], "+", RowBox[List["171872217090", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["38481075360", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["29847903120", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["34249358304", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["9764549088", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["1267977216", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["83394816", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["2682368", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["33280", " ", SuperscriptBox["z", "10"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List["1", ",", FractionBox["z", "2"]]], "]"]]]], RowBox[List["26942232382065", " ", SuperscriptBox["z", "4"]]]]]]]]]]

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]