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http://functions.wolfram.com/03.14.20.0007.01
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D[KelvinBer[z], {z, \[Alpha]}] ==
(2^(1/2 + 2 \[Alpha]) Pi^2 HypergeometricPFQRegularized[{1/4, 3/4},
{1/2, 1/4 - \[Alpha]/4, 1/2 - \[Alpha]/4, 3/4 - \[Alpha]/4,
1 - \[Alpha]/4}, -(z^4/256)])/z^\[Alpha]
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Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "\[Alpha]"]], "}"]]], RowBox[List["KelvinBer", "[", "z", "]"]]]], "\[Equal]", "\n", RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["2", " ", "\[Alpha]"]]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "4"], "-", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List["1", "-", FractionBox["\[Alpha]", "4"]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]]]], "]"]]]]]]]]
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<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> ∂ </mo> <mi> α </mi> </msup> <mrow> <mi> ber </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> z </mi> <mi> α </mi> </msup> </mrow> </mfrac> <mo>  </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mi> α </mi> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 5 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> - </mo> <mfrac> <mi> α </mi> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mfrac> <mi> α </mi> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> - </mo> <mfrac> <mi> α </mi> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> α </mi> <mn> 4 </mn> </mfrac> </mrow> </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["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox[OverscriptBox["F", "~"], "5"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "4"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "4"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "4"], "-", FractionBox["\[Alpha]", "4"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Alpha]", "4"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Alpha]", "4"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Alpha]", "4"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], 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> α </ci> </degree> </bvar> <apply> <ci> KelvinBer </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> α </ci> </apply> </apply> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <cn type='rational'> 1 <sep /> 4 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> α </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> α </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='rational'> 3 <sep /> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> α </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> α </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </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>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["KelvinBer", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["2", " ", "\[Alpha]"]]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "4"], "-", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "-", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List["1", "-", FractionBox["\[Alpha]", "4"]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]]]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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