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http://functions.wolfram.com/07.25.03.ampj.01
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HypergeometricPFQ[{9/2, 5}, {-(11/2), -(11/2)}, -z] ==
(1/34037647875) (34037647875 - 25317258750 z + 20628877500 z^2 -
25540515000 z^3 + 61297236000 z^4 - 416821204800 z^5 +
26398676304000 z^6 - 1364239285920000 z^7 + 7106917487443200 z^8 -
12543698267251200 z^9 + 10539431454827520 z^10 - 4942306507622400 z^11 +
1413257752166400 z^12 - 259734044344320 z^13 + 31625330688000 z^14 -
2586643347456 z^15 + 141905756160 z^16 - 5121162240 z^17 +
115984384 z^18 - 1486848 z^19 + 8192 z^20) -
(1/34037647875) ((512 Sqrt[Pi] (369212256000 z^(13/2) -
5858167795200 z^(15/2) + 21430961596800 z^(17/2) -
31971876249600 z^(19/2) + 24462991828800 z^(21/2) -
10838291184000 z^(23/2) + 2988258829920 z^(25/2) -
535955978880 z^(27/2) + 64167180210 z^(29/2) - 5185886580 z^(31/2) +
282051105 z^(33/2) - 10114104 z^(35/2) + 227976 z^(37/2) -
2912 z^(39/2) + 16 z^(41/2)) Erfi[Sqrt[z]])/E^z)
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<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> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 5 </mn> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </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[FractionBox["9", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], 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<mrow> <mn> 8192 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 20 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1486848 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 19 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 115984384 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 18 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5121162240 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 17 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 141905756160 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 16 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2586643347456 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 15 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 31625330688000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 14 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 259734044344320 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1413257752166400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4942306507622400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10539431454827520 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 12543698267251200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7106917487443200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1364239285920000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 26398676304000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 416821204800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 61297236000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 25540515000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20628877500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 25317258750 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 34037647875 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 34037647875 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 512 </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> 16 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 41 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2912 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 39 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 227976 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 37 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10114104 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 35 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 282051105 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 33 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5185886580 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 31 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 64167180210 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 29 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 535955978880 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 27 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2988258829920 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10838291184000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 23 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 24462991828800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 21 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 31971876249600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 19 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 21430961596800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5858167795200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 369212256000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </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='rational'> 9 <sep /> 2 </cn> <cn type='integer'> 5 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <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 /> 34037647875 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 8192 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 20 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1486848 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 19 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 115984384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 18 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5121162240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 17 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 141905756160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 16 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2586643347456 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 15 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 31625330688000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 14 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 259734044344320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1413257752166400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4942306507622400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 10539431454827520 </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'> 12543698267251200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7106917487443200 </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'> 1364239285920000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 26398676304000 </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'> 416821204800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 61297236000 </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'> 25540515000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 20628877500 </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'> 25317258750 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 34037647875 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 34037647875 </cn> <apply> <times /> <cn type='integer'> 512 </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'> 16 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 41 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2912 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 39 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 227976 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 37 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10114104 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 35 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 282051105 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 33 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5185886580 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 31 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 64167180210 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 29 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 535955978880 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 27 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2988258829920 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 25 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10838291184000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 23 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 24462991828800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 21 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 31971876249600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 21430961596800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5858167795200 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 369212256000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <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>
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Date Added to functions.wolfram.com (modification date)
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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,...,ap},{b1,...,bq},z] | |
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