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variants of this functions
HypergeometricPFQRegularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Specific values > Specialized values > Case q+1F~qat z==1





http://functions.wolfram.com/07.32.03.0031.01









  


  








Input Form





HypergeometricPFQRegularized[{-n, Subscript[a, 2], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[a, 2] - Subscript[n, 2], \[Ellipsis], Subscript[a, q + 1] - Subscript[n, q + 1]}, 1] == (-1)^\[Sigma] (n!/Product[Gamma[Subscript[a, j]], {j, 2, q + 1}]) ((1/2) Sum[Subscript[n, k] (Subscript[n, k] - 1) Sum[(Subscript[a, j] - Subscript[a, j + 1] + Subscript[n, j + 1]) (Sum[Subscript[a, j] - Subscript[a, j + 1] + Subscript[n, j + 1], {j, 1, k - 1}] - 1), {j, 1, k - 1}], {k, 2, q + 1}] + Sum[Subscript[n, k] Sum[(Subscript[a, j] - Subscript[a, j + 1] + Subscript[n, j + 1]) Sum[Subscript[n, l] (Sum[Subscript[a, j] - Subscript[a, j + 1] + Subscript[n, j + 1], {j, 1, l - 1}] - 1), {l, k + 1, q + 1}], {j, 1, k - 1}], {k, 2, q + 1}]) /; \[Sigma] == n + 2 && Subscript[a, 1] == -n && Element[Subscript[n, j], Integers] && Subscript[n, j] > 0 && 2 <= j <= q + 1 && \[Sigma] == Sum[Subscript[n, j], {j, 2, q + 1}]








Standard Form





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MathML Form







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</mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <msub> <mi> n </mi> <mi> k </mi> </msub> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mrow> <mi> j </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msub> <mi> n </mi> <mrow> <mi> j </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> l </mi> <mo> = </mo> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <msub> <mi> n </mi> <mi> l </mi> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> l </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mrow> <mi> j </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msub> <mi> n </mi> <mrow> <mi> j </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> &#963; </mi> <mo> &#10869; </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> n </mi> <mi> j </mi> </msub> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mn> 2 </mn> <mo> &#8804; </mo> <mi> j </mi> <mo> &#8804; </mo> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> &#963; </mi> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </munderover> <msub> <mi> n </mi> <mi> j </mi> </msub> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; 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</ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> j </ci> </apply> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> <apply> <leq /> <cn type='integer'> 2 </cn> <ci> j </ci> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <eq /> <ci> &#963; </ci> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </uplimit> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> j </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29