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variants of this functions
KelvinBei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBei[z] > Differentiation > Fractional integro-differentiation





http://functions.wolfram.com/03.13.20.0007.01









  


  










Input Form





D[KelvinBei[z], {z, \[Alpha]}] == z^(2 - \[Alpha]) 2^(-(11/2) + 2 \[Alpha]) Pi^2 HypergeometricPFQRegularized[{3/4, 5/4}, {3/2, (3 - \[Alpha])/4, 1 - \[Alpha]/4, (5 - \[Alpha])/4, (6 - \[Alpha])/4}, -(z^4/256)]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "\[Alpha]"]], "}"]]], RowBox[List["KelvinBei", "[", "z", "]"]]]], "\[Equal]", "\n", RowBox[List[SuperscriptBox["z", RowBox[List["2", "-", "\[Alpha]"]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], "+", RowBox[List["2", " ", "\[Alpha]"]]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "4"], ",", RowBox[List["1", "-", FractionBox["\[Alpha]", "4"]]], ",", FractionBox[RowBox[List["5", "-", "\[Alpha]"]], "4"], ",", FractionBox[RowBox[List["6", "-", "\[Alpha]"]], "4"]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]]]], "]"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mi> &#945; </mi> </msup> <mrow> <mi> bei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mi> &#945; </mi> </msup> </mrow> </mfrac> <mo> &#63449; </mo> <mrow> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> &#945; </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mn> 2 </mn> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#945; </mi> </mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 5 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> - </mo> <mi> &#945; </mi> </mrow> <mn> 4 </mn> </mfrac> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> - </mo> <mi> &#945; </mi> </mrow> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 6 </mn> <mo> - </mo> <mi> &#945; </mi> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mn> 256 </mn> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;2&quot;], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&quot;], &quot;5&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;3&quot;, &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;5&quot;, &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;3&quot;, &quot;2&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;3&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;]], &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, FractionBox[&quot;\[Alpha]&quot;, &quot;4&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;5&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;]], &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;6&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;]], &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[SuperscriptBox[&quot;z&quot;, &quot;4&quot;], &quot;256&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQRegularized] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> &#945; </ci> </degree> </bvar> <apply> <ci> KelvinBei </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#945; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <cn type='rational'> 3 <sep /> 4 </cn> <cn type='rational'> 5 <sep /> 4 </cn> </list> <list> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 256 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["KelvinBei", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", RowBox[List["2", "-", "\[Alpha]"]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], "+", RowBox[List["2", " ", "\[Alpha]"]]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "4"], ",", RowBox[List["1", "-", FractionBox["\[Alpha]", "4"]]], ",", FractionBox[RowBox[List["5", "-", "\[Alpha]"]], "4"], ",", FractionBox[RowBox[List["6", "-", "\[Alpha]"]], "4"]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]]]], "]"]]]]]]]]










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





2007-05-02





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