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variants of this functions
MeijerG






Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Integration > Definite integration > Generalization of classical Meijer's integral from two G functions > Main formulas





http://functions.wolfram.com/07.34.21.0013.01









  


  










Input Form





Integrate[\[Tau]^(\[Alpha] - 1) MeijerG[{{Subscript[c, 1], \[Ellipsis], Subscript[c, t]}, {Subscript[c, t + 1], \[Ellipsis], Subscript[c, u]}}, {{Subscript[d, 1], \[Ellipsis], Subscript[d, s]}, {Subscript[d, s + 1], \[Ellipsis], Subscript[d, v]}}, \[Sigma] \[Tau]] MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, p]}}, {{Subscript[b, 1], \[Ellipsis], Subscript[b, m]}, {Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, \[Omega] \[Tau]^(l/k)], {\[Tau], 0, Infinity}] == (((k^\[Mu] l^(\[Rho] + \[Alpha] (v - u) - 1))/ (2 Pi)^(SuperStar[b] (l - 1) + SuperStar[c] (k - 1))) MeijerG[{{Subscript[a, 1]/k, \[Ellipsis], (Subscript[a, 1] + k - 1)/k, \[Ellipsis], Subscript[a, n]/k, \[Ellipsis], (Subscript[a, n] + k - 1)/ k, (1 - \[Alpha] - Subscript[d, 1])/l, \[Ellipsis], (l - \[Alpha] - Subscript[d, 1])/l, \[Ellipsis], (1 - \[Alpha] - Subscript[d, s])/l, \[Ellipsis], (l - \[Alpha] - Subscript[d, s])/l}, {(1 - \[Alpha] - Subscript[d, s + 1])/l, \[Ellipsis], (l - \[Alpha] - Subscript[d, s + 1])/l, \[Ellipsis], (1 - \[Alpha] - Subscript[d, v])/l, \[Ellipsis], (l - \[Alpha] - Subscript[d, v])/l, Subscript[a, n + 1]/k, \[Ellipsis], (Subscript[a, n + 1] + k - 1)/k, \[Ellipsis], Subscript[a, p]/k, \[Ellipsis], (Subscript[a, p] + k - 1)/k}}, {{Subscript[b, 1]/k, \[Ellipsis], (Subscript[b, 1] + k - 1)/k, \[Ellipsis], Subscript[b, m]/k, \[Ellipsis], (Subscript[b, m] + k - 1)/ k, (1 - \[Alpha] - Subscript[c, 1])/l, \[Ellipsis], (l - \[Alpha] - Subscript[c, 1])/l, \[Ellipsis], (1 - \[Alpha] - Subscript[c, t])/l, \[Ellipsis], (l - \[Alpha] - Subscript[c, t])/l}, {(1 - \[Alpha] - Subscript[c, t + 1])/l, \[Ellipsis], (l - \[Alpha] - Subscript[c, t + 1])/l, \[Ellipsis], (1 - \[Alpha] - Subscript[c, u])/l, \[Ellipsis], (l - \[Alpha] - Subscript[c, u])/l, Subscript[b, m + 1]/k, \[Ellipsis], (Subscript[b, m + 1] + k - 1)/k, \[Ellipsis], Subscript[b, q]/k, \[Ellipsis], (Subscript[b, q] + k - 1)/k}}, (\[Omega]^k k^(k (p - q)))/(\[Sigma]^l l^(l (u - v)))])/ \[Sigma]^\[Alpha] /; Element[k, Integers] && k > 0 && Element[l, Integers] && l > 0 && GCD[k, l] == 1 && \[DoubleStruckCapitalC]\[DoubleStruckCapitalC]










Standard Form





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MathML Form







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</mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <msub> <mi> a </mi> <mi> n </mi> </msub> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> k </mi> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mn> 1 </mn> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mn> 1 </mn> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mi> s </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mi> s </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mrow> <mi> s </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mrow> <mi> s </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mi> v </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mi> v </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mfrac> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <mi> k </mi> <mo> - 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<mo> /; </mo> <mtext> &#62371; </mtext> <mrow> <mrow> <mi> k </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> l </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mi> l </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mi> &#8450;&#8450; </mi> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mi> &#8734; </mi> </msubsup> <mrow> <mrow> <msup> <mi> &#964; </mi> <mrow> <mi> &#945; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mi> u </mi> <mo> , </mo> <mi> v </mi> </mrow> <mrow> <mi> s </mi> <mo> , </mo> <mi> t </mi> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#963; </mi> <mo> &#8290; </mo> <mi> &#964; </mi> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> c </mi> <mi> t </mi> </msub> <mo> , </mo> <msub> <mi> c </mi> <mrow> <mi> t </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> c </mi> <mi> u </mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> d </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> d </mi> <mi> s </mi> </msub> <mo> , </mo> <msub> <mi> d </mi> <mrow> <mi> s </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> d </mi> <mi> v </mi> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;u&quot;, &quot;,&quot;, &quot;v&quot;]], RowBox[List[&quot;s&quot;, &quot;,&quot;, &quot;t&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;\[Sigma]&quot;, &quot; &quot;, &quot;\[Tau]&quot;]], MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[SubscriptBox[&quot;c&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;c&quot;, &quot;t&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;c&quot;, RowBox[List[&quot;t&quot;, &quot;+&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;c&quot;, &quot;u&quot;], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox[&quot;d&quot;, &quot;1&quot;], MeijerG, Rule[Editable, 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<msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> n </mi> </msub> <mo> , </mo> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> m </mi> </msub> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;p&quot;, &quot;,&quot;, &quot;q&quot;]], RowBox[List[&quot;m&quot;, &quot;,&quot;, &quot;n&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;\[Omega]&quot;, &quot; &quot;, SuperscriptBox[&quot;\[Tau]&quot;, RowBox[List[&quot;l&quot;, &quot;/&quot;, &quot;k&quot;]]]]], MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;n&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;p&quot;], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox[&quot;b&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, 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</mrow> </msup> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> l </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mo> * </mo> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> c </mi> <mo> * </mo> </msup> </mrow> </mrow> </msup> </mfrac> <mo> &#8290; </mo> <msup> <mi> &#963; </mi> <mrow> <mo> - </mo> <mi> &#945; </mi> </mrow> </msup> </mrow> </mrow> <mtext> </mtext> </mrow> <mo> &#8290; </mo> <mtext> &#62371; </mtext> <mrow> <mtext> </mtext> <mrow> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mrow> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mi> l </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> , </mo> <mrow> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mi> l </mi> <mo> &#8290; </mo> <mi> u </mi> </mrow> </mrow> </mrow> <mrow> <mrow> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mi> l </mi> <mo> &#8290; </mo> <mi> t </mi> </mrow> </mrow> <mo> , </mo> <mrow> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> + </mo> <mrow> <mi> l </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mi> &#969; </mi> <mi> k </mi> </msup> <mo> &#8290; </mo> <msup> <mi> k </mi> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> - </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> <mrow> <msup> <mi> &#963; </mi> <mi> l </mi> </msup> <mo> &#8290; </mo> <msup> <mi> l </mi> <mrow> <mi> l </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> u </mi> <mo> - </mo> <mi> v </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> </mfrac> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mfrac> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <msub> <mi> a </mi> <mi> n </mi> </msub> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <msub> <mi> a </mi> <mi> n </mi> </msub> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> k </mi> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mn> 1 </mn> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mn> 1 </mn> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mi> s </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mi> s </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mrow> <mi> s </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mrow> <mi> s </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mi> v </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> d </mi> <mi> v </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mfrac> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <msub> <mi> a </mi> <mi> p </mi> </msub> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <msub> <mi> a </mi> <mi> p </mi> </msub> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> k </mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <msub> <mi> b </mi> <mi> m </mi> </msub> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <msub> <mi> b </mi> <mi> m </mi> </msub> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> k </mi> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mn> 1 </mn> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mn> 1 </mn> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mi> t </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mi> t </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mrow> <mi> t </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mrow> <mi> t </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mi> u </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mi> u </mi> </msub> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mfrac> <msub> <mi> b </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> 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</math>










Rule Form





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





2001-10-29





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