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=3, b1`>=-11/2 > For fixed z and a1=3, b1=-9/2





http://functions.wolfram.com/07.22.03.3940.01









  


  








Input Form





HypergeometricPFQ[{3}, {-(9/2), -(5/2)}, z] == (1/14175) (32 Pi z^(5/2) (4 z^3 StruveL[-12, 2 Sqrt[z]] + 188 z^(5/2) StruveL[-11, 2 Sqrt[z]] + 3219 z^2 StruveL[-10, 2 Sqrt[z]] + 25176 z^(3/2) StruveL[-9, 2 Sqrt[z]] + 92220 z StruveL[-8, 2 Sqrt[z]] + 144000 Sqrt[z] StruveL[-7, 2 Sqrt[z]] + 70200 StruveL[-6, 2 Sqrt[z]]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "3", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "14175"], RowBox[List["(", RowBox[List["32", " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", "3"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "12"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["188", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "11"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["3219", " ", SuperscriptBox["z", "2"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "10"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["25176", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "9"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["92220", " ", "z", " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "8"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["144000", " ", SqrtBox["z"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "7"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["70200", " ", 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> 3 </mn> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 5 </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;3&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;5&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> <mfrac> <mn> 1 </mn> <mn> 14175 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 32 </mn> <mo> &#8290; </mo> <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> 4 </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> 188 </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> 3219 </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> 25176 </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> 92220 </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> 144000 </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> 70200 </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> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 3 </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'> 5 <sep /> 2 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 14175 </cn> <apply> <times /> <cn type='integer'> 32 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </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'> 188 </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'> 3219 </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'> 25176 </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'> 92220 </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'> 144000 </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'> 70200 </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> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "3", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["32", " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", "3"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "12"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["188", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "11"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["3219", " ", SuperscriptBox["z", "2"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "10"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["25176", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "9"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["92220", " ", "z", " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "8"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["144000", " ", SqrtBox["z"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "7"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["70200", " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", "6"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]]]], "14175"]]]]]


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





2007-05-02