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
MeijerG






Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Specific values > Specialized values > Cases with arbitrary {m,n,p,q} > Case {m,n,p,q}={1,n,n,n}





http://functions.wolfram.com/07.34.03.0019.01









  


  










Input Form





MeijerG[{{2 + Subscript[b, 1], \[Ellipsis], 2 + Subscript[b, r + 1], 1 + Subscript[b, r + 2], \[Ellipsis], 1 + Subscript[b, n]}, {}}, {{0}, {Subscript[b, 1], \[Ellipsis], Subscript[b, n - 1]}}, z] == ((-1)^(r - 1)/z) ((-(1/z)) Sum[(Pochhammer[r, k]/k!) PolyLog[n - k - 1, -z], {k, 0, n - 2}] + Sum[(((-1)^(r - k) Pochhammer[n - 1, k])/k!) PolyLog[r - k, -z], {k, 0, r - 1}] - Binomial[r + n - 2, r]) /; Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] == Subscript[b, n - 1] == -2










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["2", "+", SubscriptBox["b", "1"]]], ",", "\[Ellipsis]", ",", RowBox[List["2", "+", SubscriptBox["b", RowBox[List["r", "+", "1"]]]]], ",", RowBox[List["1", "+", SubscriptBox["b", RowBox[List["r", "+", "2"]]]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "+", SubscriptBox["b", "n"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", RowBox[List["n", "-", "1"]]]]], "}"]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["r", "-", "1"]]], "z"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "z"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "2"]]], RowBox[List[FractionBox[RowBox[List["Pochhammer", "[", RowBox[List["r", ",", "k"]], "]"]], RowBox[List["k", "!"]]], RowBox[List["PolyLog", "[", RowBox[List[RowBox[List["n", " ", "-", "k", "-", "1"]], ",", RowBox[List["-", "z"]]]], "]"]]]]]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["r", "-", "1"]]], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["r", "-", "k"]]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "k"]], "]"]]]], RowBox[List["k", "!"]]], RowBox[List["PolyLog", "[", RowBox[List[RowBox[List["r", " ", "-", "k"]], ",", RowBox[List["-", "z"]]]], "]"]]]]]], "-", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["r", "+", "n", "-", "2"]], ",", "r"]], "]"]]]], ")"]]]]]], "/;", RowBox[List[SubscriptBox["b", "1"], "\[Equal]", SubscriptBox["b", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["b", RowBox[List["n", "-", "1"]]], "\[Equal]", RowBox[List["-", "2"]]]]]]]]










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> <msubsup> <mi> G </mi> <mrow> <mi> n </mi> <mo> , </mo> <mi> n </mi> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> n </mi> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mi> n </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;n&quot;, &quot;,&quot;, &quot;n&quot;]], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;n&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;1&quot;], &quot;+&quot;, &quot;2&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;r&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;+&quot;, &quot;2&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;r&quot;, &quot;+&quot;, &quot;2&quot;]]], &quot;+&quot;, &quot;1&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;n&quot;], &quot;+&quot;, &quot;1&quot;]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;2&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;2&quot;]], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mi> z </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> r </mi> <mo> - </mo> <mi> k </mi> </mrow> </msup> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;k&quot;], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mrow> <mi> r </mi> <mo> - </mo> <mi> k </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </munderover> <mrow> <mfrac> <semantics> <msub> <mrow> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, &quot;r&quot;, &quot;)&quot;]], &quot;k&quot;], Pochhammer] </annotation> </semantics> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> - </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mi> n </mi> <mo> + </mo> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mi> r </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;r&quot;, &quot;-&quot;, &quot;2&quot;]], Identity, Rule[Editable, True]]], List[TagBox[&quot;r&quot;, Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <mo> &#8230; </mo> <mo> &#10869; </mo> <msub> <mi> b </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mi> n </mi> <mo> , </mo> <mi> n </mi> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> n </mi> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mi> n </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;n&quot;, &quot;,&quot;, &quot;n&quot;]], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;n&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;1&quot;], &quot;+&quot;, &quot;2&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;r&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;+&quot;, &quot;2&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;r&quot;, &quot;+&quot;, &quot;2&quot;]]], &quot;+&quot;, &quot;1&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;n&quot;], &quot;+&quot;, &quot;1&quot;]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;2&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;2&quot;]], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mi> z </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> r </mi> <mo> - </mo> <mi> k </mi> </mrow> </msup> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;k&quot;], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mrow> <mi> r </mi> <mo> - </mo> <mi> k </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </munderover> <mrow> <mfrac> <semantics> <msub> <mrow> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, &quot;r&quot;, &quot;)&quot;]], &quot;k&quot;], Pochhammer] </annotation> </semantics> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> - </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mi> n </mi> <mo> + </mo> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mi> r </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;r&quot;, &quot;-&quot;, &quot;2&quot;]], Identity, Rule[Editable, True]]], List[TagBox[&quot;r&quot;, Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <mo> &#8230; </mo> <mo> &#10869; </mo> <msub> <mi> b </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["2", "+", SubscriptBox["b_", "1"]]], ",", "\[Ellipsis]_", ",", RowBox[List["2", "+", SubscriptBox["b_", RowBox[List["r_", "+", "1"]]]]], ",", RowBox[List["1", "+", SubscriptBox["b_", RowBox[List["r_", "+", "2"]]]]], ",", "\[Ellipsis]_", ",", RowBox[List["1", "+", SubscriptBox["b_", "n_"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", RowBox[List["n_", "-", "1"]]]]], "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["r", "-", "1"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "2"]]], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["r", ",", "k"]], "]"]], " ", RowBox[List["PolyLog", "[", RowBox[List[RowBox[List["n", "-", "k", "-", "1"]], ",", RowBox[List["-", "z"]]]], "]"]]]], RowBox[List["k", "!"]]]]], "z"]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["r", "-", "1"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["r", "-", "k"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "k"]], "]"]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List[RowBox[List["r", "-", "k"]], ",", RowBox[List["-", "z"]]]], "]"]]]], RowBox[List["k", "!"]]]]], "-", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["r", "+", "n", "-", "2"]], ",", "r"]], "]"]]]], ")"]]]], "z"], "/;", RowBox[List[SubscriptBox["b", "1"], "\[Equal]", SubscriptBox["b", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["b", RowBox[List["n", "-", "1"]]], "\[Equal]", RowBox[List["-", "2"]]]]]]]]]]










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





2001-10-29