Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=-11/2, b1`>=-11/2 > For fixed z and a1=-11/2, b1=-9/2





http://functions.wolfram.com/07.22.03.0383.01









  


  










Input Form





HypergeometricPFQ[{-(11/2)}, {-(9/2), 6}, z] == (1/(866206566225 z^(9/2))) (8 (BesselI[1, 2 Sqrt[z]] (163341809631000 + 118207888548750 z + 4108830350625 z^2 + 73045872900 z^3 + 1728896400 z^4 + 57153600 z^5 + 2822400 z^6 + 230400 z^7 + 36864 z^8 + 16384 z^9 + 65536 z^10 + 65536 Pi z^(21/2) StruveL[0, 2 Sqrt[z]]) - 2 Sqrt[z] BesselI[0, 2 Sqrt[z]] (81670904815500 + 18268491866625 z - 273922023375 z^2 - 5618913300 z^3 - 157172400 z^4 - 6350400 z^5 - 403200 z^6 - 46080 z^7 - 12288 z^8 - 16384 z^9 + 65536 z^10 + 32768 Pi z^10 StruveL[1, 2 Sqrt[z]])))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["-", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", "6"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["866206566225", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]], RowBox[List["(", RowBox[List["8", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["BesselI", "[", RowBox[List["1", ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]], " ", RowBox[List["(", RowBox[List["163341809631000", "+", RowBox[List["118207888548750", " ", "z"]], "+", RowBox[List["4108830350625", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["73045872900", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1728896400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["57153600", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["2822400", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["230400", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["36864", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["16384", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["65536", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["65536", " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List["0", ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]]]], "-", RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]], " ", RowBox[List["(", RowBox[List["81670904815500", "+", RowBox[List["18268491866625", " ", "z"]], "-", RowBox[List["273922023375", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["5618913300", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["157172400", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["6350400", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["403200", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["46080", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["12288", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["16384", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["65536", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["32768", " ", "\[Pi]", " ", SuperscriptBox["z", "10"], " ", RowBox[List["StruveL", "[", RowBox[List["1", ",", RowBox[List["2", " ", 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> &#8202; </mo> <mn> 1 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <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[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;1&quot;], SubscriptBox[&quot;F&quot;, &quot;2&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;11&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;9&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;6&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 866206566225 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> I </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 65536 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <msub> <mstyle fontweight='bold' fontstyle='normal'> <semantics> <mi> L </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveL </ci> </annotation-xml> </semantics> </mstyle> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 21 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 65536 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16384 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 36864 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 230400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2822400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 57153600 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1728896400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 73045872900 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4108830350625 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 118207888548750 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 163341809631000 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 32768 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <msub> <mstyle fontweight='bold' fontstyle='normal'> <semantics> <mi> L </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveL </ci> </annotation-xml> </semantics> </mstyle> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 65536 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 16384 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 12288 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 46080 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 403200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6350400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 157172400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5618913300 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 273922023375 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 18268491866625 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 81670904815500 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </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'> 11 <sep /> 2 </cn> </apply> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <cn type='integer'> 6 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 866206566225 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <plus /> <apply> <times /> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 65536 </cn> <pi /> <apply> <ci> StruveL </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 21 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 65536 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36864 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 230400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2822400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 57153600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1728896400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 73045872900 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4108830350625 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 118207888548750 </cn> <ci> z </ci> </apply> <cn type='integer'> 163341809631000 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 32768 </cn> <pi /> <apply> <ci> StruveL </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 65536 </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'> 16384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12288 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 46080 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 403200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6350400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 157172400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5618913300 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 273922023375 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 18268491866625 </cn> <ci> z </ci> </apply> <cn type='integer'> 81670904815500 </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"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", "6"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["BesselI", "[", RowBox[List["1", ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]], " ", RowBox[List["(", RowBox[List["163341809631000", "+", RowBox[List["118207888548750", " ", "z"]], "+", RowBox[List["4108830350625", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["73045872900", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1728896400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["57153600", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["2822400", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["230400", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["36864", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["16384", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["65536", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["65536", " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List["0", ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]]]], "-", RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["BesselI", "[", RowBox[List["0", ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]], " ", RowBox[List["(", RowBox[List["81670904815500", "+", RowBox[List["18268491866625", " ", "z"]], "-", RowBox[List["273922023375", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["5618913300", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["157172400", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["6350400", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["403200", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["46080", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["12288", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["16384", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["65536", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["32768", " ", "\[Pi]", " ", SuperscriptBox["z", "10"], " ", RowBox[List["StruveL", "[", RowBox[List["1", ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["866206566225", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2007-05-02