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variants of this functions
HypergeometricPFQRegularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Series representations > Generalized power series > Expansions on branch cuts for p==q+1 > For the function itself





http://functions.wolfram.com/07.32.06.0047.01









  


  








Input Form





HypergeometricPFQRegularized[{Subscript[a, 1], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == (1/Product[Gamma[Subscript[a, k]], {k, 1, q + 1}]) Sum[(1/k!) MeijerG[{{1 - Subscript[a, 1] - k, \[Ellipsis], 1 - Subscript[a, q + 1] - k}, {}}, {{0}, {1 - Subscript[b, 1] - k, \[Ellipsis], 1 - Subscript[b, q] - k}}, (-x) E^(2 Pi I Floor[Arg[x - z]/(2 Pi)])] (z - x)^k, {k, 0, Infinity}] /; x > 1








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", 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_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["aa", "1"], "-", "k"]], ",", "\[Ellipsis]", ",", RowBox[List["1", "-", SubscriptBox["a", RowBox[List["q", "+", "1"]]], "-", "k"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["bb", "1"], "-", "k"]], ",", "\[Ellipsis]", ",", RowBox[List["1", "-", SubscriptBox["bb", "q"], "-", "k"]]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List["-", "x"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["x", "-", "z"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "x"]], ")"]], "k"]]], RowBox[List["k", "!"]]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], RowBox[List["q", "+", "1"]]], RowBox[List["Gamma", "[", SubscriptBox["a", "k"], "]"]]]]], "/;", RowBox[List["x", ">", "1"]]]]]]]]


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





2007-05-02