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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] > Identities > Functional identities > Relations between contiguous functions





http://functions.wolfram.com/07.31.17.0011.01









  


  










Input Form





Product[Subscript[b, k], {k, 2, q}] (c HypergeometricPFQ[{a, b, Subscript[a, 3], \[Ellipsis], Subscript[a, p]}, {c, Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, z] - a HypergeometricPFQ[{a + 1, b + 1, Subscript[a, 3], \[Ellipsis], Subscript[a, p]}, {c + 1, Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, z] - (c - a) HypergeometricPFQ[ {a, b + 1, Subscript[a, 3], \[Ellipsis], Subscript[a, p]}, {c + 1, Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, z]) + z a Product[Subscript[a, j], {j, 3, p}] HypergeometricPFQ[ {a + 1, b + 1, Subscript[a, 3] + 1, \[Ellipsis], Subscript[a, p] + 1}, {c + 1, Subscript[b, 2] + 1, \[Ellipsis], Subscript[b, q] + 1}, z] == 0










Standard Form





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MathML Form







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</mo> <mrow> <mi> a </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 3 </mn> </mrow> <mi> p </mi> </munderover> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mi> p </mi> </msub> <msub> <mi> F </mi> <mi> q </mi> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> b </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mrow> <msub> <mi> a </mi> <mi> p </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mrow> <mi> c </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mrow> <msub> <mi> b </mi> <mi> q </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;p&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;q&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[&quot;a&quot;, &quot;+&quot;, &quot;1&quot;]], &quot;,&quot;, RowBox[List[&quot;b&quot;, &quot;+&quot;, &quot;1&quot;]], &quot;,&quot;, RowBox[List[SubscriptBox[&quot;a&quot;, &quot;3&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;p&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;;&quot;, RowBox[List[&quot;c&quot;, &quot;+&quot;, &quot;1&quot;]]]], &quot;,&quot;, RowBox[List[SubscriptBox[&quot;b&quot;, &quot;2&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;,&quot;, &quot;\[Ellipsis]&quot;, &quot;,&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;q&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;;&quot;, &quot;z&quot;]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation> </semantics> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> </annotation-xml> </semantics> </math>










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





2001-10-29