Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

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
 











SphericalBesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving sin > Linear arguments





http://functions.wolfram.com/03.21.21.0023.01









  


  










Input Form





Integrate[Sin[b + a z] SphericalBesselJ[\[Nu], a z], z] == (2^(-1 - \[Nu]) Sqrt[Pi] z (a z)^\[Nu] (a z (1 + \[Nu]) Cos[b] HypergeometricPFQ[{1 + \[Nu]/2, 1 + \[Nu]/2, 3/2 + \[Nu]/2}, {3/2, 2 + \[Nu]/2, 3/2 + \[Nu], 2 + \[Nu]}, (-a^2) z^2] + (2 + \[Nu]) HypergeometricPFQ[{1/2 + \[Nu]/2, 1/2 + \[Nu]/2, 1 + \[Nu]/2}, {1/2, 3/2 + \[Nu]/2, 1 + \[Nu], 3/2 + \[Nu]}, (-a^2) z^2] Sin[b]))/((2 + 3 \[Nu] + \[Nu]^2) Gamma[3/2 + \[Nu]])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]], " ", RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", "z"]]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]]], " ", SqrtBox["\[Pi]"], " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], "\[Nu]"], " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", "z", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["Cos", "[", "b", "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["2", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], ",", RowBox[List["2", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], " ", SuperscriptBox["z", "2"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "+", "\[Nu]"]], ",", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]]]], "}"]], ",", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], " ", SuperscriptBox["z", "2"]]]]], "]"]], " ", RowBox[List["Sin", "[", "b", "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List["3", " ", "\[Nu]"]], "+", SuperscriptBox["\[Nu]", "2"]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], "]"]]]], ")"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> j </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mi> &#957; </mi> </msup> <mtext> </mtext> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 4 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;3&quot;], SubscriptBox[&quot;F&quot;, &quot;4&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[&quot;\[Nu]&quot;, &quot;2&quot;], &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;\[Nu]&quot;, &quot;2&quot;], &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;\[Nu]&quot;, &quot;2&quot;], &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[TagBox[RowBox[List[TagBox[FractionBox[&quot;3&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;\[Nu]&quot;, &quot;2&quot;], &quot;+&quot;, &quot;2&quot;]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;\[Nu]&quot;, &quot;+&quot;, FractionBox[&quot;3&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;\[Nu]&quot;, &quot;+&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[RowBox[List[RowBox[List[&quot;-&quot;, SuperscriptBox[&quot;a&quot;, &quot;2&quot;]]], &quot; &quot;, SuperscriptBox[&quot;z&quot;, &quot;2&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> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 4 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;3&quot;], SubscriptBox[&quot;F&quot;, &quot;4&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[&quot;\[Nu]&quot;, &quot;2&quot;], &quot;+&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;\[Nu]&quot;, &quot;2&quot;], &quot;+&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;\[Nu]&quot;, &quot;2&quot;], &quot;+&quot;, &quot;1&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[FractionBox[&quot;1&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;\[Nu]&quot;, &quot;2&quot;], &quot;+&quot;, FractionBox[&quot;3&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;\[Nu]&quot;, &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;\[Nu]&quot;, &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[RowBox[List[RowBox[List[&quot;-&quot;, SuperscriptBox[&quot;a&quot;, &quot;2&quot;]]], &quot; &quot;, SuperscriptBox[&quot;z&quot;, &quot;2&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> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <sin /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> SphericalBesselJ </ci> <ci> &#957; </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> <apply> <power /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <ci> &#957; </ci> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <cos /> <ci> b </ci> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </list> <list> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <sin /> <ci> b </ci> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Sin", "[", RowBox[List["b_", "+", RowBox[List["a_", " ", "z_"]]]], "]"]], " ", RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", RowBox[List["a_", " ", "z_"]]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]]], " ", SqrtBox["\[Pi]"], " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], "\[Nu]"], " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", "z", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["Cos", "[", "b", "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["2", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], ",", RowBox[List["2", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], " ", SuperscriptBox["z", "2"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "+", "\[Nu]"]], ",", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]]]], "}"]], ",", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], " ", SuperscriptBox["z", "2"]]]]], "]"]], " ", RowBox[List["Sin", "[", "b", "]"]]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List["3", " ", "\[Nu]"]], "+", SuperscriptBox["\[Nu]", "2"]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], "]"]]]]]]]]]










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





2007-05-02





© 1998-2014 Wolfram Research, Inc.