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





http://functions.wolfram.com/07.22.03.5910.01









  


  










Input Form





HypergeometricPFQ[{6}, {-(9/2), -(3/2)}, z] == -((1/85050) (Pi z^(5/2) (32 z^4 StruveL[-14, 2 Sqrt[z]] + 3 (912 z^(7/2) StruveL[-13, 2 Sqrt[z]] + 5 (6192 z^3 StruveL[-12, 2 Sqrt[z]] + 107896 z^(5/2) StruveL[-11, 2 Sqrt[z]] + 1042230 z^2 StruveL[-10, 2 Sqrt[z]] + 5623905 z^(3/2) StruveL[-9, 2 Sqrt[z]] + 16211370 z StruveL[-8, 2 Sqrt[z]] + 22180410 Sqrt[z] StruveL[-7, 2 Sqrt[z]] + 10581480 StruveL[-6, 2 Sqrt[z]])))))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "6", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", FractionBox["3", "2"]]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", "85050"], RowBox[List["(", RowBox[List["\[Pi]", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["32", " ", SuperscriptBox["z", "4"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "14"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["912", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "13"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["6192", " ", SuperscriptBox["z", "3"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "12"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["107896", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "11"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["1042230", " ", SuperscriptBox["z", "2"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "10"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["5623905", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "9"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["16211370", " ", "z", " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "8"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["22180410", " ", SqrtBox["z"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "7"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["10581480", " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "6"]], ",", 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> <mn> 6 </mn> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> </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[&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[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[RowBox[List[&quot;-&quot;, FractionBox[&quot;3&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[&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> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 85050 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 32 </mn> <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> <mrow> <mo> - </mo> <mn> 14 </mn> </mrow> </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> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 912 </mn> <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> <mrow> <mo> - </mo> <mn> 13 </mn> </mrow> </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> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6192 </mn> <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> <mrow> <mo> - </mo> <mn> 12 </mn> </mrow> </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> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 107896 </mn> <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> <mrow> <mo> - </mo> <mn> 11 </mn> </mrow> </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> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1042230 </mn> <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> <mrow> <mo> - </mo> <mn> 10 </mn> </mrow> </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> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5623905 </mn> <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> <mrow> <mo> - </mo> <mn> 9 </mn> </mrow> </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> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16211370 </mn> <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> <mrow> <mo> - </mo> <mn> 8 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 22180410 </mn> <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> <mrow> <mo> - </mo> <mn> 7 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 10581480 </mn> <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> <mrow> <mo> - </mo> <mn> 6 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 6 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 85050 </cn> <apply> <times /> <pi /> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <ci> StruveL </ci> <cn type='integer'> -14 </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'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 912 </cn> <apply> <ci> StruveL </ci> <cn type='integer'> -13 </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'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 6192 </cn> <apply> <ci> StruveL </ci> <cn type='integer'> -12 </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'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 107896 </cn> <apply> <ci> StruveL </ci> <cn type='integer'> -11 </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'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1042230 </cn> <apply> <ci> StruveL </ci> <cn type='integer'> -10 </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'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5623905 </cn> <apply> <ci> StruveL </ci> <cn type='integer'> -9 </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'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16211370 </cn> <apply> <ci> StruveL </ci> <cn type='integer'> -8 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 22180410 </cn> <apply> <ci> StruveL </ci> <cn type='integer'> -7 </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'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10581480 </cn> <apply> <ci> StruveL </ci> <cn type='integer'> -6 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </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["{", "6", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", FractionBox["3", "2"]]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["32", " ", SuperscriptBox["z", "4"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "14"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["912", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "13"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["6192", " ", SuperscriptBox["z", "3"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "12"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["107896", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "11"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["1042230", " ", SuperscriptBox["z", "2"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "10"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["5623905", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "9"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["16211370", " ", "z", " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "8"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["22180410", " ", SqrtBox["z"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "7"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["10581480", " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "6"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "85050"]]]]]]]










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





2007-05-02