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WeierstrassPHalfPeriodValues






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassPHalfPeriodValues[{g2,g3}] > Series representations > q-series





http://functions.wolfram.com/09.20.06.0002.01









  


  










Input Form





WeierstrassPHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}] == {Pi^2/(6 Subscript[\[Omega], 1]^2) + ((4 Pi^2)/Subscript[\[Omega], 1]^2) Sum[(2 k - 1) (q^(4 k - 2)/(1 - q^(4 k - 2))), {k, 1, Infinity}], -(Pi^2/(12 Subscript[\[Omega], 1]^2)) - ((2 Pi^2)/Subscript[\[Omega], 1]^2) Sum[(-1)^k ((k q^k)/(1 + (-1)^k q^k)), {k, 1, Infinity}], -(Pi^2/(12 Subscript[\[Omega], 1]^2)) - ((2 Pi^2)/Subscript[\[Omega], 1]^2) Sum[(k q^k)/(1 + q^k), {k, 1, Infinity}]}










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["6", " ", SubsuperscriptBox["\[Omega]", "1", "2"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["4", " ", SuperscriptBox["\[Pi]", "2"]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "1"]], ")"]], " ", SuperscriptBox["q", RowBox[List[RowBox[List["4", " ", "k"]], "-", "2"]]]]], RowBox[List["1", "-", SuperscriptBox["q", RowBox[List[RowBox[List["4", " ", "k"]], "-", "2"]]]]]]]]]], SubsuperscriptBox["\[Omega]", "1", "2"]]]], ",", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["12", " ", SubsuperscriptBox["\[Omega]", "1", "2"]]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["(", RowBox[List["k", " ", SuperscriptBox["q", "k"]]], ")"]]]], RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["q", "k"]]]]]]]]]], SubsuperscriptBox["\[Omega]", "1", "2"]]]], ",", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["12", " ", SubsuperscriptBox["\[Omega]", "1", "2"]]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["k", " ", SuperscriptBox["q", "k"]]], RowBox[List["1", "+", SuperscriptBox["q", "k"]]]]]]]], SubsuperscriptBox["\[Omega]", "1", "2"]]]]]], "}"]]]]]]










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





2001-10-29





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