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variants of this functions
HypergeometricPFQRegularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > General characteristics > Branch points > With respect to z





http://functions.wolfram.com/07.32.04.0014.01









  


  








Input Form





RamificationIndex[HypergeometricPFQRegularized[{Subscript[a, 1], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z], z, 1] == s /; Subscript[\[Psi], q] == Sum[Subscript[b, j], {j, 1, q}] - Sum[Subscript[a, j], {j, 1, q + 1}] == r/s && Element[r, Integers] && Element[s - 1, Integers] && s - 1 > 0 && GCD[r, s] == 1 && NonTerminatingHypergeometricSeriesQ[ {Subscript[a, 1], \[Ellipsis], Subscript[a, q + 1]}]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", RowBox[List["q_", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]], ",", "z_"]], "]"]], ",", "z_", ",", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["s", "/;", RowBox[List[RowBox[List[SubscriptBox["\[Psi]", "q"], "\[Equal]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "q"], SubscriptBox["b", "j"]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], RowBox[List["q", "+", "1"]]], SubscriptBox["a", "j"]]]]], "\[Equal]", FractionBox["r", "s"]]], "&&", RowBox[List["r", "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["s", "-", "1"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["s", "-", "1"]], ">", "0"]], "&&", RowBox[List[RowBox[List["GCD", "[", RowBox[List["r", ",", "s"]], "]"]], "\[Equal]", "1"]], "&&", RowBox[List["NonTerminatingHypergeometricSeriesQ", "[", RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", RowBox[List["q", "+", "1"]]]]], "}"]], "]"]]]]]]]]]]


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





2001-10-29