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http://functions.wolfram.com/07.22.03.a7q2.01
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HypergeometricPFQ[{-(17/4)}, {3/2, -(23/4)}, z] ==
(1/(33229228725 z^(1/4)))
(Sqrt[2] ((-(-33229228725 + 50084634600 z + 19431336960 z^2 +
2187214848 z^3 + 104464384 z^4 + 2097152 z^5))
BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (11076409575 + 2689142400 z +
285214720 z^2 + 13287424 z^3 + 262144 z^4) BesselI[1/4, Sqrt[z]]
BesselI[5/4, Sqrt[z]] + 8 z (7960599675 + 2647612800 z + 283453440 z^2 +
13254656 z^3 + 262144 z^4) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)
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Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["-", FractionBox["17", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["-", FractionBox["23", "4"]]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["33229228725", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], RowBox[List["(", RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "33229228725"]], "+", RowBox[List["50084634600", " ", "z"]], "+", RowBox[List["19431336960", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2187214848", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["104464384", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["2097152", " ", SuperscriptBox["z", "5"]]]]], ")"]]]], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List[FractionBox["1", "4"], ",", SqrtBox["z"]]], "]"]], "2"]]], "+", RowBox[List["12", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["11076409575", "+", RowBox[List["2689142400", " ", "z"]], "+", RowBox[List["285214720", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["13287424", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["262144", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["1", "4"], ",", SqrtBox["z"]]], "]"]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["5", "4"], ",", SqrtBox["z"]]], "]"]]]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["7960599675", "+", RowBox[List["2647612800", " ", "z"]], "+", RowBox[List["283453440", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["13254656", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["262144", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List[FractionBox["5", "4"], ",", SqrtBox["z"]]], "]"]], "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["5", "4"], "]"]], "2"]]], ")"]]]]]]]]
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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> 1 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 17 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 23 </mn> <mn> 4 </mn> </mfrac> </mrow> </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["17", "4"]]], 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["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["23", "4"]]], 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> 33229228725 </mn> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2097152 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 104464384 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2187214848 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 19431336960 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 50084634600 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 33229228725 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <msup> <mrow> <msub> <mi> I </mi> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </msub> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 262144 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13287424 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 285214720 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2689142400 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 11076409575 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> </msub> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </msub> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 262144 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13254656 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 283453440 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2647612800 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 7960599675 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <msub> <mi> I </mi> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> </msub> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </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'> 17 <sep /> 4 </cn> </apply> </list> <list> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 23 <sep /> 4 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 33229228725 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2097152 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 104464384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2187214848 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19431336960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 50084634600 </cn> <ci> z </ci> </apply> <cn type='integer'> -33229228725 </cn> </apply> </apply> <apply> <power /> <apply> <ci> BesselI </ci> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 262144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13287424 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 285214720 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2689142400 </cn> <ci> z </ci> </apply> <cn type='integer'> 11076409575 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='rational'> 5 <sep /> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> BesselI </ci> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 262144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13254656 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 283453440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2647612800 </cn> <ci> z </ci> </apply> <cn type='integer'> 7960599675 </cn> </apply> <apply> <power /> <apply> <ci> BesselI </ci> <cn type='rational'> 5 <sep /> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["-", FractionBox["17", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["-", FractionBox["23", "4"]]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "33229228725"]], "+", RowBox[List["50084634600", " ", "z"]], "+", RowBox[List["19431336960", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2187214848", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["104464384", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["2097152", " ", SuperscriptBox["z", "5"]]]]], ")"]]]], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List[FractionBox["1", "4"], ",", SqrtBox["z"]]], "]"]], "2"]]], "+", RowBox[List["12", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["11076409575", "+", RowBox[List["2689142400", " ", "z"]], "+", RowBox[List["285214720", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["13287424", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["262144", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["1", "4"], ",", SqrtBox["z"]]], "]"]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["5", "4"], ",", SqrtBox["z"]]], "]"]]]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["7960599675", "+", RowBox[List["2647612800", " ", "z"]], "+", RowBox[List["283453440", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["13254656", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["262144", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List[FractionBox["5", "4"], ",", SqrtBox["z"]]], "]"]], "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["5", "4"], "]"]], "2"]]], RowBox[List["33229228725", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]]]] |
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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,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,...,ap},{b1,...,bq},z] | |
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