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variants of this functions
InverseWeierstrassP






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseWeierstrassP[z,{g2,g3}] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/09.22.06.0001.01









  


  










Input Form





InverseWeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] == SeriesData[$CellContext`z, ComplexInfinity, {1, 0, 0, 0, Rational[1, 40] Subscript[$CellContext`g, 2], 0, Rational[1, 56] Subscript[$CellContext`g, 3], 0, Rational[1, 384] Subscript[$CellContext`g, 2]^2, 0, Rational[3, 704] Subscript[$CellContext`g, 2] Subscript[$CellContext`g, 3], 0, Rational[1, 13312] (5 Subscript[$CellContext`g, 2]^3 + 24 Subscript[$CellContext`g, 3]^2), 0, Rational[1, 1024] Subscript[$CellContext`g, 2]^2 Subscript[$CellContext`g, 3], 0, Rational[5, 557056] (7 Subscript[$CellContext`g, 2]^4 + 96 Subscript[$CellContext`g, 2] Subscript[$CellContext`g, 3]^2), 0, Rational[5, 155648] (7 Subscript[$CellContext`g, 2]^3 Subscript[$CellContext`g, 3] + 8 Subscript[$CellContext`g, 3]^3), 0, Rational[1, 262144] (3 Subscript[$CellContext`g, 2]^5 + 80 Subscript[$CellContext`g, 2]^2 Subscript[$CellContext`g, 3]^2)}, 1, 23, 2]










Standard Form





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MathML Form







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</apply> </apply> </apply> </apply> </list> <cn type='integer'> 1 </cn> <cn type='integer'> 23 </cn> <cn type='integer'> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseWeierstrassP", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List[SqrtBox[FractionBox["1", "$CellContext`z"]], "+", FractionBox[RowBox[List[FractionBox["1", "40"], " ", SubscriptBox["$CellContext`g", "2"]]], SuperscriptBox["$CellContext`z", RowBox[List["5", "/", "2"]]]], "+", FractionBox[RowBox[List[FractionBox["1", "56"], " ", SubscriptBox["$CellContext`g", "3"]]], SuperscriptBox["$CellContext`z", RowBox[List["7", "/", "2"]]]], "+", FractionBox[RowBox[List[FractionBox["1", "384"], " ", SubsuperscriptBox["$CellContext`g", "2", "2"]]], SuperscriptBox["$CellContext`z", RowBox[List["9", "/", "2"]]]], "+", FractionBox[RowBox[List[FractionBox["3", "704"], " ", SubscriptBox["$CellContext`g", "2"], " ", SubscriptBox["$CellContext`g", "3"]]], SuperscriptBox["$CellContext`z", RowBox[List["11", "/", "2"]]]], "+", FractionBox[RowBox[List[FractionBox["1", "13312"], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SubsuperscriptBox["$CellContext`g", "2", "3"]]], "+", RowBox[List["24", " ", SubsuperscriptBox["$CellContext`g", "3", "2"]]]]], ")"]]]], SuperscriptBox["$CellContext`z", RowBox[List["13", "/", "2"]]]], "+", FractionBox[RowBox[List[FractionBox["1", "1024"], " ", SubsuperscriptBox["$CellContext`g", "2", "2"], " ", SubscriptBox["$CellContext`g", "3"]]], SuperscriptBox["$CellContext`z", RowBox[List["15", "/", "2"]]]], "+", FractionBox[RowBox[List[FractionBox["5", "557056"], " ", RowBox[List["(", RowBox[List[RowBox[List["7", " ", SubsuperscriptBox["$CellContext`g", "2", "4"]]], "+", RowBox[List["96", " ", SubscriptBox["$CellContext`g", "2"], " ", SubsuperscriptBox["$CellContext`g", "3", "2"]]]]], ")"]]]], SuperscriptBox["$CellContext`z", RowBox[List["17", "/", "2"]]]], "+", FractionBox[RowBox[List[FractionBox["5", "155648"], " ", RowBox[List["(", RowBox[List[RowBox[List["7", " ", SubsuperscriptBox["$CellContext`g", "2", "3"], " ", SubscriptBox["$CellContext`g", "3"]]], "+", RowBox[List["8", " ", SubsuperscriptBox["$CellContext`g", "3", "3"]]]]], ")"]]]], SuperscriptBox["$CellContext`z", RowBox[List["19", "/", "2"]]]], "+", FractionBox[RowBox[List[FractionBox["1", "262144"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SubsuperscriptBox["$CellContext`g", "2", "5"]]], "+", RowBox[List["80", " ", SubsuperscriptBox["$CellContext`g", "2", "2"], " ", SubsuperscriptBox["$CellContext`g", "3", "2"]]]]], ")"]]]], SuperscriptBox["$CellContext`z", RowBox[List["21", "/", "2"]]]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", FractionBox["1", "$CellContext`z"], "]"]], RowBox[List["23", "/", "2"]]], SeriesData[$CellContext`z, DirectedInfinity[], List[], 1, 23, 2], Rule[Editable, False]]]], SeriesData[$CellContext`z, DirectedInfinity[], List[1, 0, 0, 0, Times[Rational[1, 40], Subscript[$CellContext`g, 2]], 0, Times[Rational[1, 56], Subscript[$CellContext`g, 3]], 0, Times[Rational[1, 384], Power[Subscript[$CellContext`g, 2], 2]], 0, Times[Rational[3, 704], Subscript[$CellContext`g, 2], Subscript[$CellContext`g, 3]], 0, Times[Rational[1, 13312], Plus[Times[5, Power[Subscript[$CellContext`g, 2], 3]], Times[24, Power[Subscript[$CellContext`g, 3], 2]]]], 0, Times[Rational[1, 1024], Power[Subscript[$CellContext`g, 2], 2], Subscript[$CellContext`g, 3]], 0, Times[Rational[5, 557056], Plus[Times[7, Power[Subscript[$CellContext`g, 2], 4]], Times[96, Subscript[$CellContext`g, 2], Power[Subscript[$CellContext`g, 3], 2]]]], 0, Times[Rational[5, 155648], Plus[Times[7, Power[Subscript[$CellContext`g, 2], 3], Subscript[$CellContext`g, 3]], Times[8, Power[Subscript[$CellContext`g, 3], 3]]]], 0, Times[Rational[1, 262144], Plus[Times[3, Power[Subscript[$CellContext`g, 2], 5]], Times[80, Power[Subscript[$CellContext`g, 2], 2], Power[Subscript[$CellContext`g, 3], 2]]]]], 1, 23, 2], Rule[Editable, False]]]]]]










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





2001-10-29





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