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,a2,a3},{b1,b2},z] > Specific values > For some numeric parameters and fixed z > For fixed z and a1=5/6, a2=1, a3=7/6





http://functions.wolfram.com/07.27.03.0502.01









  


  










Input Form





HypergeometricPFQ[{5/6, 1, 7/6}, {11/6, 13/6}, z] == (35/(24 z^(7/6))) (12 z^(1/6) - 2 Sqrt[3] (1 + z^(1/3)) ArcTan[1 - z^(1/3), Sqrt[3] z^(1/6)] + (-1 + z^(1/3)) (2 Log[(1 + z^(1/6))/(1 - z^(1/6))] + Log[(1 + z^(1/6) + z^(1/3))/(1 - z^(1/6) + z^(1/3))])) /; !IntervalMemberQ[Interval[{1, Infinity}], z]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "6"], ",", "1", ",", FractionBox["7", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["11", "6"], ",", FractionBox["13", "6"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["35", RowBox[List["24", " ", SuperscriptBox["z", RowBox[List["7", "/", "6"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["12", " ", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]], "-", RowBox[List["2", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ",", RowBox[List[SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]], RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]]], "]"]]]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "6"]]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "6"]]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]], "]"]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", " ", "z"]], "]"]], "]"]]]]]]










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> <mfrac> <mn> 5 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 6 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 11 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 13 </mn> <mn> 6 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </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[FractionBox[&quot;5&quot;, &quot;6&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;1&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;7&quot;, &quot;6&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;11&quot;, &quot;6&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;13&quot;, &quot;6&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[&quot;z&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> <mfrac> <mn> 35 </mn> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 6 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> </mrow> <mo> , </mo> <mrow> <msqrt> <mn> 3 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> + </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> - </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <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> <mfrac> <mn> 5 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 6 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 11 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 13 </mn> <mn> 6 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </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[FractionBox[&quot;5&quot;, &quot;6&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;1&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;7&quot;, &quot;6&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;11&quot;, &quot;6&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;13&quot;, &quot;6&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[&quot;z&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> <mfrac> <mn> 35 </mn> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 6 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> </mrow> <mo> , </mo> <mrow> <msqrt> <mn> 3 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> + </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> - </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 6 </mn> </mroot> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "6"], ",", "1", ",", FractionBox["7", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["11", "6"], ",", FractionBox["13", "6"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List[RowBox[List["12", " ", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]], "-", RowBox[List["2", " ", SqrtBox["3"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ",", RowBox[List[SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]], RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "6"]]]]]], "]"]]]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "6"]]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "6"]]], "+", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]], "]"]]]], ")"]]]]]], ")"]]]], RowBox[List["24", " ", SuperscriptBox["z", RowBox[List["7", "/", "6"]]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]










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





2001-10-29