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Mathematica Notation

Traditional Notation

Hypergeometric Functions > HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] > Specific values > Specialized values > Case q+1Fq




Input Form

HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], \[Ellipsis], Subscript[a, q + 1]}, {1 + Subscript[a, 1], 1 + Subscript[a, 2], \[Ellipsis], 1 + Subscript[a, q]}, z] == (m^q/Gamma[m]) Sum[StirlingS1[m, j] LerchPhi[z, q - j + 1, m], {j, 0, m}] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, q + 1] == m && Element[m, Integers] && m > 0

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["a", RowBox[List["q", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "2"]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "+", SubscriptBox["a", "q"]]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox["m", "q"], RowBox[List["Gamma", "[", "m", "]"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "m"], " ", RowBox[List[RowBox[List["StirlingS1", "[", RowBox[List["m", ",", "j"]], "]"]], " ", RowBox[List["LerchPhi", "[", RowBox[List["z", ",", RowBox[List["q", "-", "j", "+", "1"]], ",", "m"]], "]"]]]]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "\[Equal]", SubscriptBox["a", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["a", RowBox[List["q", "+", "1"]]], "\[Equal]", "m"]], "\[And]", RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

MathML Form

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