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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/07.31.03.0025.01









  


  










Input Form





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










Standard Form





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MathML Form







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</mo> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mfrac> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <msub> <mi> n </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> n </mi> <mi> k </mi> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <msub> <mi> n </mi> <mi> k </mi> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mfrac> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> n </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mi> j </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;n&quot;, &quot;k&quot;]]], &quot;)&quot;]], &quot;j&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> <mi> j </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, SubscriptBox[&quot;a&quot;, &quot;k&quot;], &quot;)&quot;]], &quot;j&quot;], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> j </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, &quot;k&quot;], &quot;-&quot;, &quot;a&quot;, &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;j&quot;], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <munder> <mrow> <mi> l </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mrow> <mi> l </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> </munder> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </munderover> <mfrac> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <msub> <mi> a </mi> <mi> l </mi> </msub> <mo> ) </mo> </mrow> <msub> <mi> n </mi> <mi> l </mi> </msub> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, SubscriptBox[&quot;a&quot;, &quot;l&quot;], &quot;)&quot;]], SubscriptBox[&quot;n&quot;, &quot;l&quot;]], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> l </mi> </msub> <mo> - </mo> <msub> <mi> n </mi> <mi> l </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> j </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, &quot;k&quot;], &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;l&quot;], &quot;-&quot;, SubscriptBox[&quot;n&quot;, &quot;l&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;j&quot;], Pochhammer] </annotation> </semantics> </mrow> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> l </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> <msub> <mi> n </mi> <mi> l </mi> </msub> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, &quot;l&quot;], &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;k&quot;]]], &quot;)&quot;]], SubscriptBox[&quot;n&quot;, &quot;l&quot;]], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> l </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> j </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, &quot;k&quot;], &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;l&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;j&quot;], Pochhammer] </annotation> </semantics> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &lt; </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> <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> </mrow> </mrow> </annotation-xml> </semantics> </math>










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





2001-10-29





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