Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

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
KelvinKei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[z] > Series representations > Generalized power series > Expansions at z==0 > For small integer powers of the function





http://functions.wolfram.com/03.15.06.0016.01









  


  










Input Form





KelvinKei[z]^2 \[Proportional] (1/32) (Pi^2 + (-4 EulerGamma + Log[16])^2 + 16 (2 EulerGamma + Log[z/4]) Log[z] + (1/32) (16 EulerGamma^2 + Pi^2 - 8 EulerGamma (5 + Log[16]) + 8 (4 + 2 Log[2]^2 + Log[32]) + 8 Log[z] (-5 + 4 EulerGamma - 4 Log[2] + 2 Log[z])) z^4 + (1/221184) (536 + 9 Pi^2 + 12 EulerGamma (-43 + 12 EulerGamma - 24 Log[2]) + 516 Log[2] + Log[4096]^2 + 12 Log[z] (-43 + 24 EulerGamma - 24 Log[2] + 12 Log[z])) z^8 + \[Ellipsis]) - (1/32) ((4 EulerGamma - Pi - 4 Log[2] + 4 Log[z]) (4 EulerGamma + Pi - 4 Log[2] + 4 Log[z]) + (1/32) (3 Pi^2 - 8 (4 + 6 Log[2]^2 + Log[2048]) + 8 EulerGamma (11 - 6 EulerGamma + Log[4096]) + 8 (11 - 12 EulerGamma + Log[4096] - 6 Log[z]) Log[z]) z^4 + (1/221184) (1680 EulerGamma^2 - 105 Pi^2 - 4 EulerGamma (1217 + 840 Log[2]) + 4 (838 + Log[2] (1217 + 420 Log[2])) + 4 Log[z] (-1217 + 840 EulerGamma - 840 Log[2] + 420 Log[z])) z^8 + \[Ellipsis]) - ((Pi z^2)/16) (1 + z^4/216 + z^8/432000 + \[Ellipsis]) + ((Pi z^2)/32) (-2 + 4 EulerGamma - 4 Log[2] + 4 Log[z] + (1/864) (73 - 60 EulerGamma + 60 Log[2] - 60 Log[z]) z^4 + (7/204800) (-(4127/630) + 4 EulerGamma - 4 Log[2] + 4 Log[z]) z^8 + \[Ellipsis]) /; (z -> 0)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["KelvinKei", "[", "z", "]"]], "2"], "\[Proportional]", RowBox[List[RowBox[List[FractionBox["1", "32"], RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], "+", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "EulerGamma"]], "+", RowBox[List["Log", "[", "16", "]"]]]], ")"]], "2"], "+", RowBox[List["16", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "EulerGamma"]], "+", RowBox[List["Log", "[", FractionBox["z", "4"], "]"]]]], ")"]], " ", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List[FractionBox["1", "32"], " ", RowBox[List["(", RowBox[List[RowBox[List["16", " ", SuperscriptBox["EulerGamma", "2"]]], "+", SuperscriptBox["\[Pi]", "2"], "-", RowBox[List["8", " ", "EulerGamma", " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["Log", "[", "16", "]"]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["(", RowBox[List["4", "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["Log", "[", "2", "]"]], "2"]]], "+", RowBox[List["Log", "[", "32", "]"]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "EulerGamma"]], "-", RowBox[List["4", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]]]]]], ")"]], SuperscriptBox["z", "4"]]], " ", "+", RowBox[List[FractionBox["1", "221184"], RowBox[List["(", RowBox[List["536", "+", RowBox[List["9", " ", SuperscriptBox["\[Pi]", "2"]]], "+", RowBox[List["12", " ", "EulerGamma", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "43"]], "+", RowBox[List["12", " ", "EulerGamma"]], "-", RowBox[List["24", " ", RowBox[List["Log", "[", "2", "]"]]]]]], ")"]]]], "+", RowBox[List["516", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", SuperscriptBox[RowBox[List["Log", "[", "4096", "]"]], "2"], "+", RowBox[List["12", " ", RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "43"]], "+", RowBox[List["24", " ", "EulerGamma"]], "-", RowBox[List["24", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["12", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]]]]]], ")"]], SuperscriptBox["z", "8"]]], " ", "+", "\[Ellipsis]"]], ")"]]]], "-", RowBox[List[FractionBox["1", "32"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["4", " ", "EulerGamma"]], "-", "\[Pi]", "-", RowBox[List["4", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "EulerGamma"]], "+", "\[Pi]", "-", RowBox[List["4", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "32"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"]]], "-", RowBox[List["8", " ", RowBox[List["(", RowBox[List["4", "+", RowBox[List["6", " ", SuperscriptBox[RowBox[List["Log", "[", "2", "]"]], "2"]]], "+", RowBox[List["Log", "[", "2048", "]"]]]], ")"]]]], "+", RowBox[List["8", " ", "EulerGamma", " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["6", " ", "EulerGamma"]], "+", RowBox[List["Log", "[", "4096", "]"]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["12", " ", "EulerGamma"]], "+", RowBox[List["Log", "[", "4096", "]"]], "-", RowBox[List["6", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]], " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]], SuperscriptBox["z", "4"]]], "+", " ", RowBox[List[FractionBox["1", "221184"], RowBox[List["(", RowBox[List[RowBox[List["1680", " ", SuperscriptBox["EulerGamma", "2"]]], "-", RowBox[List["105", " ", SuperscriptBox["\[Pi]", "2"]]], "-", RowBox[List["4", " ", "EulerGamma", " ", RowBox[List["(", RowBox[List["1217", "+", RowBox[List["840", " ", RowBox[List["Log", "[", "2", "]"]]]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List["838", "+", RowBox[List[RowBox[List["Log", "[", "2", "]"]], " ", RowBox[List["(", RowBox[List["1217", "+", RowBox[List["420", " ", RowBox[List["Log", "[", "2", "]"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1217"]], "+", RowBox[List["840", " ", "EulerGamma"]], "-", RowBox[List["840", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["420", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]]]]]], ")"]], SuperscriptBox["z", "8"]]], "+", "\[Ellipsis]"]], ")"]]]], "-", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", SuperscriptBox["z", "2"]]], "16"], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", "4"], "216"], "+", FractionBox[SuperscriptBox["z", "8"], "432000"], "+", "\[Ellipsis]"]], ")"]]]], "+", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", SuperscriptBox["z", "2"]]], "32"], RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["4", " ", "EulerGamma"]], "-", RowBox[List["4", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List[FractionBox["1", "864"], RowBox[List["(", RowBox[List["73", "-", RowBox[List["60", " ", "EulerGamma"]], "+", RowBox[List["60", " ", RowBox[List["Log", "[", "2", "]"]]]], "-", RowBox[List["60", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]], SuperscriptBox["z", "4"]]], "+", RowBox[List[FractionBox[RowBox[List["7", " "]], "204800"], RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["4127", "630"]]], "+", RowBox[List["4", " ", "EulerGamma"]], "-", RowBox[List["4", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]], SuperscriptBox["z", "8"]]], "+", "\[Ellipsis]"]], ")"]]]]]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "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> <msup> <mrow> <mi> kei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8733; </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 32 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 16 </mn> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 32 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 16 </mn> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <msup> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 32 </mn> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 221184 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mn> 4096 </mn> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 516 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 24 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> <mo> - </mo> <mn> 43 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 24 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> <mo> - </mo> <mn> 43 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 536 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 32 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> &#960; </mi> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> &#960; </mi> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 32 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2048 </mn> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 4096 </mn> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 4096 </mn> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 221184 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 840 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1217 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 1680 </mn> <mo> &#8290; </mo> <msup> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 105 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 420 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1217 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 838 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 840 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 420 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 840 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> <mo> - </mo> <mn> 1217 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 16 </mn> </mfrac> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mn> 216 </mn> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 8 </mn> </msup> <mn> 432000 </mn> </mfrac> <mo> + </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 32 </mn> </mfrac> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> <mo> - </mo> <mn> 2 </mn> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 864 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> <mo> + </mo> <mn> 73 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 204800 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mn> 4127 </mn> <mn> 630 </mn> </mfrac> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <power /> <apply> <ci> KelvinKei </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 32 </cn> <apply> <plus /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ln /> <cn type='integer'> 16 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <eulergamma /> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <apply> <ln /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <eulergamma /> </apply> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 32 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -8 </cn> <eulergamma /> <apply> <plus /> <apply> <ln /> <cn type='integer'> 16 </cn> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <eulergamma /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ln /> <cn type='integer'> 32 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ln /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <eulergamma /> </apply> <cn type='integer'> -5 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 221184 </cn> <apply> <plus /> <apply> <power /> <apply> <ln /> <cn type='integer'> 4096 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 516 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <eulergamma /> <apply> <plus /> <apply> <times /> <cn type='integer'> -24 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <eulergamma /> </apply> <cn type='integer'> -43 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <ln /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -24 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 24 </cn> <eulergamma /> </apply> <cn type='integer'> -43 </cn> </apply> </apply> <cn type='integer'> 536 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 32 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <eulergamma /> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> <pi /> <apply> <times /> <cn type='integer'> 4 </cn> <eulergamma /> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 32 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ln /> <cn type='integer'> 2048 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <eulergamma /> <apply> <plus /> <apply> <ln /> <cn type='integer'> 4096 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <eulergamma /> </apply> </apply> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ln /> <ci> z </ci> </apply> <apply> <plus /> <apply> <ln /> <cn type='integer'> 4096 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <eulergamma /> </apply> </apply> <cn type='integer'> 11 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 221184 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <eulergamma /> <apply> <plus /> <apply> <times /> <cn type='integer'> 840 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1217 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1680 </cn> <apply> <power /> <eulergamma /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 105 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 420 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1217 </cn> </apply> </apply> <cn type='integer'> 838 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ln /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -840 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 420 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 840 </cn> <eulergamma /> </apply> <cn type='integer'> -1217 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 16 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 216 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <cn type='integer'> 432000 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 32 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <eulergamma /> </apply> <cn type='integer'> -2 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 864 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 60 </cn> <eulergamma /> </apply> </apply> <cn type='integer'> 73 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 7 <sep /> 204800 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 4127 <sep /> 630 </cn> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <eulergamma /> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["KelvinKei", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "32"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], "+", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "EulerGamma"]], "+", RowBox[List["Log", "[", "16", "]"]]]], ")"]], "2"], "+", RowBox[List["16", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "EulerGamma"]], "+", RowBox[List["Log", "[", FractionBox["z", "4"], "]"]]]], ")"]], " ", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List[FractionBox["1", "32"], " ", RowBox[List["(", RowBox[List[RowBox[List["16", " ", SuperscriptBox["EulerGamma", "2"]]], "+", SuperscriptBox["\[Pi]", "2"], "-", RowBox[List["8", " ", "EulerGamma", " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["Log", "[", "16", "]"]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["(", RowBox[List["4", "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["Log", "[", "2", "]"]], "2"]]], "+", RowBox[List["Log", "[", "32", "]"]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "EulerGamma"]], "-", RowBox[List["4", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["z", "4"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["536", "+", RowBox[List["9", " ", SuperscriptBox["\[Pi]", "2"]]], "+", RowBox[List["12", " ", "EulerGamma", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "43"]], "+", RowBox[List["12", " ", "EulerGamma"]], "-", RowBox[List["24", " ", RowBox[List["Log", "[", "2", "]"]]]]]], ")"]]]], "+", RowBox[List["516", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", SuperscriptBox[RowBox[List["Log", "[", "4096", "]"]], "2"], "+", RowBox[List["12", " ", RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "43"]], "+", RowBox[List["24", " ", "EulerGamma"]], "-", RowBox[List["24", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["12", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["z", "8"]]], "221184"], "+", "\[Ellipsis]"]], ")"]]]], "-", RowBox[List[FractionBox["1", "32"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["4", " ", "EulerGamma"]], "-", "\[Pi]", "-", RowBox[List["4", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "EulerGamma"]], "+", "\[Pi]", "-", RowBox[List["4", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "32"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"]]], "-", RowBox[List["8", " ", RowBox[List["(", RowBox[List["4", "+", RowBox[List["6", " ", SuperscriptBox[RowBox[List["Log", "[", "2", "]"]], "2"]]], "+", RowBox[List["Log", "[", "2048", "]"]]]], ")"]]]], "+", RowBox[List["8", " ", "EulerGamma", " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["6", " ", "EulerGamma"]], "+", RowBox[List["Log", "[", "4096", "]"]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["12", " ", "EulerGamma"]], "+", RowBox[List["Log", "[", "4096", "]"]], "-", RowBox[List["6", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]], " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]], " ", SuperscriptBox["z", "4"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["1680", " ", SuperscriptBox["EulerGamma", "2"]]], "-", RowBox[List["105", " ", SuperscriptBox["\[Pi]", "2"]]], "-", RowBox[List["4", " ", "EulerGamma", " ", RowBox[List["(", RowBox[List["1217", "+", RowBox[List["840", " ", RowBox[List["Log", "[", "2", "]"]]]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List["838", "+", RowBox[List[RowBox[List["Log", "[", "2", "]"]], " ", RowBox[List["(", RowBox[List["1217", "+", RowBox[List["420", " ", RowBox[List["Log", "[", "2", "]"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1217"]], "+", RowBox[List["840", " ", "EulerGamma"]], "-", RowBox[List["840", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["420", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["z", "8"]]], "221184"], "+", "\[Ellipsis]"]], ")"]]]], "-", RowBox[List[FractionBox["1", "16"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", "4"], "216"], "+", FractionBox[SuperscriptBox["z", "8"], "432000"], "+", "\[Ellipsis]"]], ")"]]]], "+", RowBox[List[FractionBox["1", "32"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["4", " ", "EulerGamma"]], "-", RowBox[List["4", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List[FractionBox["1", "864"], " ", RowBox[List["(", RowBox[List["73", "-", RowBox[List["60", " ", "EulerGamma"]], "+", RowBox[List["60", " ", RowBox[List["Log", "[", "2", "]"]]]], "-", RowBox[List["60", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]], " ", SuperscriptBox["z", "4"]]], "+", FractionBox[RowBox[List["7", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["4127", "630"]]], "+", RowBox[List["4", " ", "EulerGamma"]], "-", RowBox[List["4", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]], " ", SuperscriptBox["z", "8"]]], "204800"], "+", "\[Ellipsis]"]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]]]










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





2007-05-02





© 1998-2014 Wolfram Research, Inc.