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 EllipticTheta

 http://functions.wolfram.com/09.04.06.0002.01

 Input Form

 EllipticTheta[4, z, q] == Sum[(-1)^k q^k^2 E^(2 k I z), {k, -Infinity, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z", ",", "q"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], SuperscriptBox["q", SuperscriptBox["k", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", "k", " ", "\[ImaginaryI]", " ", "z"]]]]]]]]]]]

 MathML Form

 ϑ 4 ( z , q ) k = - ( - 1 ) k q k 2 2 k z EllipticTheta 4 z q k -1 -1 k q k 2 2 k z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z_", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["q", SuperscriptBox["k", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "k", " ", "\[ImaginaryI]", " ", "z"]]]]]]]]]]]

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

 2001-10-29

© 1998-2013 Wolfram Research, Inc.