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 EllipticTheta

 http://functions.wolfram.com/09.04.27.0002.02

 Input Form

 EllipticTheta[4, z, q] == EllipticTheta[3, z + (2 m + 1) (Pi/2), q] /; Element[m, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z", ",", "q"]], "]"]], "\[Equal]", RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", RowBox[List["z", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "m"]], "+", "1"]], ")"]], " ", FractionBox["\[Pi]", "2"]]]]], ",", "q"]], "]"]]]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]

 MathML Form

 ϑ 4 ( z , q ) ϑ 3 ( π 2 ( 2 m + 1 ) + z , q ) /; m TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition EllipticTheta 4 z q EllipticTheta 3 2 -1 2 m 1 z q m [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z_", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", RowBox[List["z", "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m"]], "+", "1"]], ")"]], " ", "\[Pi]"]]]], ",", "q"]], "]"]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]]]

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

 2001-10-29