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=1/4, a2=m/4, a3=1





http://functions.wolfram.com/07.27.03.0347.01









  


  










Input Form





HypergeometricPFQ[{1/4, 1, 1}, {5/4, 2}, z] == (1/(3 z)) ((-z^(3/4)) Log[1 - z^(1/4)] + I z^(3/4) Log[1 - I z^(1/4)] - I z^(3/4) Log[1 + I z^(1/4)] + z^(3/4) Log[1 + z^(1/4)] + Log[1 - z])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", "1", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "4"], ",", "2"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["3", " ", "z"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List["1", "-", "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> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mn> 2 </mn> </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;1&quot;, &quot;4&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;1&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;1&quot;, HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;5&quot;, &quot;4&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;2&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> 1 </mn> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 1 <sep /> 4 </cn> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> </list> <list> <cn type='rational'> 5 <sep /> 4 </cn> <cn type='integer'> 2 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <ln /> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </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["{", RowBox[List[FractionBox["1", "4"], ",", "1", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "4"], ",", "2"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]]]], RowBox[List["3", " ", "z"]]]]]]]










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





2001-10-29