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,...,ap},{b1,...,bq},z] > Specific values > Specialized values > Case 3F2





http://functions.wolfram.com/07.31.03.0127.01









  


  








Input Form





HypergeometricPFQ[{a, b, c}, {d, e}, 1] == Sqrt[Gamma[1 - a]] Sqrt[Gamma[1 - b]] Sqrt[Gamma[1 - c]] Gamma[d] Gamma[e] Sqrt[Gamma[d + e - a - b - c]] (ClebschGordan[{(d - a - b - 1)/2, (b + d - a - 1)/2}, {(e - a - c - 1)/2, (a + 1 - c - e)/2}, {(d + e - b - c)/2 - 1, (b + d - c - e)/2}]/(Sqrt[-1 - b - c + d + e] Sqrt[Gamma[-a + d]] Sqrt[Gamma[-b + d]] Sqrt[Gamma[-c + d]] Sqrt[Gamma[-a + e]] Sqrt[Gamma[-b + e]] Sqrt[Gamma[-c + e]])) /; Re[d + e - a - b - c] > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["a", ",", "b", ",", "c"]], "}"]], ",", RowBox[List["{", RowBox[List["d", ",", "e"]], "}"]], ",", "1"]], "]"]], "\[Equal]", RowBox[List[SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", "a"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", "b"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", "c"]], "]"]]], " ", RowBox[List["Gamma", "[", "d", "]"]], " ", RowBox[List["Gamma", "[", "e", "]"]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["d", "+", "e", "-", "a", "-", "b", "-", "c"]], "]"]]], " ", RowBox[List[RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["d", "-", "a", "-", "b", "-", "1"]], "2"], ",", FractionBox[RowBox[List["b", "+", "d", "-", "a", "-", "1"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["e", "-", "a", "-", "c", "-", "1"]], "2"], ",", FractionBox[RowBox[List["a", "+", "1", "-", "c", "-", "e"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox[RowBox[List["d", "+", "e", "-", "b", "-", "c"]], "2"], "-", "1"]], ",", FractionBox[RowBox[List["b", "+", "d", "-", "c", "-", "e"]], "2"]]], "}"]]]], "]"]], "/", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "b", "-", "c", "+", "d", "+", "e"]]], SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "a"]], "+", "d"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "b"]], "+", "d"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "c"]], "+", "d"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "a"]], "+", "e"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "b"]], "+", "e"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "c"]], "+", "e"]], "]"]]]]], ")"]]]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", RowBox[List["d", "+", "e", "-", "a", "-", "b", "-", "c"]], "]"]], ">", "0"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> <mo> , </mo> <mi> c </mi> </mrow> <mo> ; </mo> <mrow> <mi> d </mi> <mo> , </mo> <mi> e </mi> </mrow> <mo> ; </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;3&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;2&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[&quot;a&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;b&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;c&quot;, HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[&quot;d&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;e&quot;, HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[&quot;1&quot;, HypergeometricPFQ, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> d </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> e </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mi> d </mi> <mo> + </mo> <mi> e </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <semantics> <mrow> <mo> &#9001; </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mfrac> <mrow> <mi> e </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mfrac> <mrow> <mi> b </mi> <mo> + </mo> <mi> d </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mfrac> <mrow> <mi> a </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mi> e </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mtext> &#8287; </mtext> <mo> &#10072; </mo> <mtext> &#8287; </mtext> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mfrac> <mrow> <mi> e </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> - </mo> <mi> b </mi> <mo> - </mo> <mi> c </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mtext> </mtext> <mo> - </mo> <mrow> <mn> 1 </mn> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mfrac> <mrow> <mi> b </mi> <mo> + </mo> <mi> d </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mi> e </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mrow> <mtext> </mtext> <mo> &#9002; </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[LeftAngleBracket]&quot;, RowBox[List[RowBox[List[FractionBox[RowBox[List[&quot;d&quot;, &quot;-&quot;, &quot;a&quot;, &quot;-&quot;, &quot;b&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;2&quot;], &quot;\[MediumSpace]&quot;, FractionBox[RowBox[List[&quot;e&quot;, &quot;-&quot;, &quot;a&quot;, &quot;-&quot;, &quot;c&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;2&quot;], &quot; \[MediumSpace]&quot;, FractionBox[RowBox[List[&quot;b&quot;, &quot;+&quot;, &quot;d&quot;, &quot;-&quot;, &quot;a&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;2&quot;], &quot; \[MediumSpace]&quot;, FractionBox[RowBox[List[&quot;a&quot;, &quot;-&quot;, &quot;c&quot;, &quot;-&quot;, &quot;e&quot;, &quot;+&quot;, &quot;1&quot;]], &quot;2&quot;]]], &quot; \[MediumSpace]&quot;, &quot;\[VerticalSeparator]&quot;, &quot;\[MediumSpace]&quot;, RowBox[List[RowBox[List[FractionBox[RowBox[List[&quot;d&quot;, &quot;-&quot;, &quot;a&quot;, &quot;-&quot;, &quot;b&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;2&quot;], &quot; \[MediumSpace]&quot;, FractionBox[RowBox[List[&quot;e&quot;, &quot;-&quot;, &quot;a&quot;, &quot;-&quot;, &quot;c&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;2&quot;], &quot; \[MediumSpace]&quot;, FractionBox[RowBox[List[&quot;d&quot;, &quot;+&quot;, &quot;e&quot;, &quot;-&quot;, &quot;b&quot;, &quot;-&quot;, &quot;c&quot;]], &quot;2&quot;]]], &quot; &quot;, &quot;-&quot;, RowBox[List[&quot;1&quot;, &quot;\[MediumSpace]&quot;, FractionBox[RowBox[List[&quot;b&quot;, &quot;+&quot;, &quot;d&quot;, &quot;-&quot;, &quot;c&quot;, &quot;-&quot;, &quot;e&quot;]], &quot;2&quot;]]]]]]], &quot; &quot;, &quot;\[RightAngleBracket]&quot;]], ClebschGordan, Rule[StripWrapperBoxes, True]] </annotation> </semantics> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> - </mo> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> b </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <ci> a </ci> <ci> b </ci> <ci> c </ci> </list> <list> <ci> d </ci> <ci> e </ci> </list> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Gamma </ci> <ci> d </ci> </apply> <apply> <ci> Gamma </ci> <ci> e </ci> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <ci> d </ci> <ci> e </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <apply> <ci> ClebschGordan </ci> <apply> <ci> AngleBracket </ci> <apply> <ci> VerticalSeparator </ci> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> e </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> e </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <gt /> <apply> <real /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["a_", ",", "b_", ",", "c_"]], "}"]], ",", RowBox[List["{", RowBox[List["d_", ",", "e_"]], "}"]], ",", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", "a"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", "b"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", "c"]], "]"]]], " ", RowBox[List["Gamma", "[", "d", "]"]], " ", RowBox[List["Gamma", "[", "e", "]"]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["d", "+", "e", "-", "a", "-", "b", "-", "c"]], "]"]]], " ", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["d", "-", "a", "-", "b", "-", "1"]], ")"]]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["b", "+", "d", "-", "a", "-", "1"]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["e", "-", "a", "-", "c", "-", "1"]], ")"]]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["a", "+", "1", "-", "c", "-", "e"]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["d", "+", "e", "-", "b", "-", "c"]], ")"]]]], "-", "1"]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["b", "+", "d", "-", "c", "-", "e"]], ")"]]]]]], "}"]]]], "]"]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "b", "-", "c", "+", "d", "+", "e"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "a"]], "+", "d"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "b"]], "+", "d"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "c"]], "+", "d"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "a"]], "+", "e"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "b"]], "+", "e"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "c"]], "+", "e"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", RowBox[List["d", "+", "e", "-", "a", "-", "b", "-", "c"]], "]"]], ">", "0"]]]]]]]]


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





2001-10-29