Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ans8)

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=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.ans8.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(9/2), -(7/2)}, z] == (1/1406514375) (1406514375 + 2946982500 z + 7662154500 z^2 + 40864824000 z^3 + 1042053012000 z^4 - 79196028912000 z^5 - 1418328881424000 z^6 - 4912689050035200 z^7 - 6810921779961600 z^8 - 4848400474444800 z^9 - 2009656172160000 z^10 - 521710679347200 z^11 - 88645126348800 z^12 - 10110197744640 z^13 - 782192920320 z^14 - 40899484800 z^15 - 1415247360 z^16 - 30882816 z^17 - 382976 z^18 - 2048 z^19) - (1/1406514375) (64 E^z Sqrt[Pi] (4799759328000 z^(11/2) + 41905591056000 z^(13/2) + 111379030560000 z^(15/2) + 134737135344000 z^(17/2) + 88585889112000 z^(19/2) + 34936798629600 z^(21/2) + 8778036355200 z^(23/2) + 1458661591800 z^(25/2) + 163788732450 z^(27/2) + 12530811195 z^(29/2) + 649877130 z^(31/2) + 22351560 z^(33/2) + 485520 z^(35/2) + 6000 z^(37/2) + 32 z^(39/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Erf </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[FractionBox["11", "2"], ",", "6"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["1406514375", "+", RowBox[List["2946982500", " ", "z"]], "+", RowBox[List["7662154500", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["40864824000", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1042053012000", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["79196028912000", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["1418328881424000", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["4912689050035200", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["6810921779961600", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["4848400474444800", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["2009656172160000", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["521710679347200", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["88645126348800", " ", SuperscriptBox["z", "12"]]], "-", RowBox[List["10110197744640", " ", SuperscriptBox["z", "13"]]], "-", RowBox[List["782192920320", " ", SuperscriptBox["z", "14"]]], "-", RowBox[List["40899484800", " ", SuperscriptBox["z", "15"]]], "-", RowBox[List["1415247360", " ", SuperscriptBox["z", "16"]]], "-", RowBox[List["30882816", " ", SuperscriptBox["z", "17"]]], "-", RowBox[List["382976", " ", SuperscriptBox["z", "18"]]], "-", RowBox[List["2048", " ", SuperscriptBox["z", "19"]]]]], "1406514375"], "-", FractionBox[RowBox[List["64", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["4799759328000", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["41905591056000", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["111379030560000", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["134737135344000", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "+", RowBox[List["88585889112000", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "+", RowBox[List["34936798629600", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]], "+", RowBox[List["8778036355200", " ", SuperscriptBox["z", RowBox[List["23", "/", "2"]]]]], "+", RowBox[List["1458661591800", " ", SuperscriptBox["z", RowBox[List["25", "/", "2"]]]]], "+", RowBox[List["163788732450", " ", SuperscriptBox["z", RowBox[List["27", "/", "2"]]]]], "+", RowBox[List["12530811195", " ", SuperscriptBox["z", RowBox[List["29", "/", "2"]]]]], "+", RowBox[List["649877130", " ", SuperscriptBox["z", RowBox[List["31", "/", "2"]]]]], "+", RowBox[List["22351560", " ", SuperscriptBox["z", RowBox[List["33", "/", "2"]]]]], "+", RowBox[List["485520", " ", SuperscriptBox["z", RowBox[List["35", "/", "2"]]]]], "+", RowBox[List["6000", " ", SuperscriptBox["z", RowBox[List["37", "/", "2"]]]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["39", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]], "1406514375"]]]]]]]

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]