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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/07.31.03.0026.01









  


  








Input Form





HypergeometricPFQ[{1, Subscript[a, 2], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[a, 2] + 1, \[Ellipsis], Subscript[a, q + 1] + 1}, 1] == (-Product[Subscript[a, j], {j, 2, q + 1}]) Sum[Product[If[l == k, 1, PolyGamma[Subscript[a, k]]/ (Subscript[a, l] - Subscript[a, k])], {l, 2, q + 1}], {k, 2, q + 1}] /; Subscript[a, l] != Subscript[a, k] && 2 <= l <= q + 1 && 2 <= k <= q + 1 && l != k








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", 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[RowBox[List["-", RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], RowBox[List["q", "+", "1"]]], SubscriptBox["a", "j"]]], ")"]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "2"]], RowBox[List["q", "+", "1"]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["l", "=", "2"]], RowBox[List["q", "+", "1"]]], RowBox[List["If", "[", RowBox[List[RowBox[List["l", "\[Equal]", "k"]], ",", "1", ",", FractionBox[RowBox[List["PolyGamma", "[", SubscriptBox["a", "k"], "]"]], RowBox[List[SubscriptBox["a", "l"], "-", SubscriptBox["a", "k"]]]]]], "]"]]]]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["a", "l"], "\[NotEqual]", SubscriptBox["a", "k"]]], "\[And]", RowBox[List["2", "\[LessEqual]", "l", "\[LessEqual]", RowBox[List["q", "+", "1"]]]], "\[And]", RowBox[List["2", "\[LessEqual]", "k", "\[LessEqual]", RowBox[List["q", "+", "1"]]]], "\[And]", RowBox[List["l", "\[NotEqual]", "k"]]]]]]]]








MathML Form







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





2001-10-29