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 EllipticTheta

 http://functions.wolfram.com/09.01.04.0003.01

 Input Form

 EllipticTheta[1, z, -q] == Exp[(-((I Pi)/4)) Sign[Im[q]]] EllipticTheta[1, z, q]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", RowBox[List["-", "q"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Exp", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "4"]]], " ", RowBox[List["Sign", "[", RowBox[List["Im", "[", "q", "]"]], "]"]]]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]]]]]]]

 MathML Form

 ϑ 1 ( z , - q ) exp ( - π 4 sgn ( Im ( q ) ) ) ϑ 1 ( z , q ) EllipticTheta 1 z -1 q -1 4 -1 Sign q EllipticTheta 1 z q [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z_", ",", RowBox[List["-", "q_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["-", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], ")"]]]], ")"]], " ", RowBox[List["Sign", "[", RowBox[List["Im", "[", "q", "]"]], "]"]]]]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]]]]]]]

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

 2001-10-29