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,...,ap},{b1,...,bq},z] > Specific values > Specialized values > Case q+1Fqat z==1





http://functions.wolfram.com/07.31.03.0036.01









  


  










Input Form





HypergeometricPFQ[{-n, Subscript[a, 2], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[a, 2] - 1, \[Ellipsis], Subscript[a, q + 1] - 1}, 1] == S[q, n] /; Subscript[a, 2] == Subscript[a, 3] == \[Ellipsis] == Subscript[a, q + 1] == a && S[q, 0] == 1 && (S[q, n] == 0 /; n > q) && S[q, q] == q/(1 - a)^q && S[q, q - 1] == (q! ((3 - q)/2 - a))/(1 - a)^q && S[q, q - 2] == (q!/((1 - a)^q 24)) (12 (a + q - 3) (a - 1) + (q - 2) (3 q - 5)) && S[q, n] == ((a + n - 1)/(a - 1)) S[q - 1, n] - (n/(a - 1)) S[q - 1, n - 1] && Element[n, Integers] && n > 0










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "n"]], ",", SubscriptBox["a", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["a", RowBox[List["q", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["a", "2"], "-", "1"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", RowBox[List["q", "+", "1"]]], "-", "1"]]]], "}"]], ",", "1"]], "]"]], "\[Equal]", RowBox[List["S", "[", RowBox[List["q", ",", "n"]], "]"]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["a", "2"], "\[Equal]", SubscriptBox["a", "3"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["a", RowBox[List["q", "+", "1"]]], "\[Equal]", "a"]], "\[And]", RowBox[List[RowBox[List["S", "[", RowBox[List["q", ",", "0"]], "]"]], "\[Equal]", "1"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["S", "[", RowBox[List["q", ",", "n"]], "]"]], "\[Equal]", "0"]], "/;", RowBox[List["n", ">", "q"]]]], ")"]], "\[And]", RowBox[List[RowBox[List["S", "[", RowBox[List["q", ",", "q"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "a"]], ")"]], RowBox[List["-", "q"]]], "q"]]]], "\[And]", RowBox[List[RowBox[List["S", "[", RowBox[List["q", ",", RowBox[List["q", "-", "1"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "a"]], ")"]], RowBox[List["-", "q"]]], RowBox[List["q", "!"]], RowBox[List["(", RowBox[List[FractionBox[RowBox[List["3", "-", "q"]], "2"], "-", "a"]], ")"]]]]]], "\[And]", RowBox[List[RowBox[List["S", "[", RowBox[List["q", ",", RowBox[List["q", "-", "2"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["q", "!"]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "a"]], ")"]], RowBox[List["-", "q"]]]]], "24"], RowBox[List["(", RowBox[List[RowBox[List["12", RowBox[List["(", RowBox[List["a", "+", "q", "-", "3"]], ")"]], RowBox[List["(", RowBox[List["a", "-", "1"]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["q", "-", "2"]], ")"]], RowBox[List["(", RowBox[List[RowBox[List["3", "q"]], "-", "5"]], ")"]]]]]], ")"]]]]]], "\[And]", RowBox[List[RowBox[List["S", "[", RowBox[List["q", ",", "n"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox[RowBox[List["a", "+", "n", "-", "1"]], RowBox[List["a", "-", "1"]]], RowBox[List["S", "[", RowBox[List[RowBox[List["q", "-", "1"]], ",", "n"]], "]"]]]], "-", RowBox[List[FractionBox["n", RowBox[List["a", "-", "1"]]], RowBox[List["S", "[", RowBox[List[RowBox[List["q", "-", "1"]], ",", RowBox[List["n", "-", "1"]]]], "]"]]]]]]]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "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> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <msub> <mi> F </mi> <mi> q </mi> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ; </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mrow> <msub> <mi> a </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[RowBox[List[&quot;q&quot;, &quot;+&quot;, &quot;1&quot;]], TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;q&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;-&quot;, &quot;n&quot;]], &quot;,&quot;, SubscriptBox[&quot;a&quot;, &quot;2&quot;], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, RowBox[List[&quot;q&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;;&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, &quot;2&quot;], &quot;-&quot;, &quot;1&quot;]]]], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;a&quot;, RowBox[List[&quot;q&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;-&quot;, &quot;1&quot;]], &quot;;&quot;, TagBox[&quot;1&quot;, HypergeometricPFQ, Rule[Editable, True]]]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#10869; </mo> <mo> &#8230; </mo> <mo> &#10869; </mo> <msub> <mi> a </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> &#10869; </mo> <mi> a </mi> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &gt; </mo> <mi> q </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> &#8290; </mo> <mi> q </mi> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> q </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 3 </mn> <mo> - </mo> <mi> q </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mrow> <mi> q </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> ! </mo> </mrow> <mn> 24 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> q </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mi> n </mi> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <msub> <mi> F </mi> <mi> q </mi> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ; </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mrow> <msub> <mi> a </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[RowBox[List[&quot;q&quot;, &quot;+&quot;, &quot;1&quot;]], TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;q&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;-&quot;, &quot;n&quot;]], &quot;,&quot;, SubscriptBox[&quot;a&quot;, &quot;2&quot;], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, RowBox[List[&quot;q&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;;&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, &quot;2&quot;], &quot;-&quot;, &quot;1&quot;]]]], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;a&quot;, RowBox[List[&quot;q&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;-&quot;, &quot;1&quot;]], &quot;;&quot;, TagBox[&quot;1&quot;, HypergeometricPFQ, Rule[Editable, True]]]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#10869; </mo> <mo> &#8230; </mo> <mo> &#10869; </mo> <msub> <mi> a </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> &#10869; </mo> <mi> a </mi> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &gt; </mo> <mi> q </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> &#8290; </mo> <mi> q </mi> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> q </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 3 </mn> <mo> - </mo> <mi> q </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mrow> <mi> q </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> ! </mo> </mrow> <mn> 24 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> q </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> q </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mi> n </mi> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mi> S </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










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





2001-10-29