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 EllipticTheta

 http://functions.wolfram.com/09.04.06.0025.01

 Input Form

 EllipticTheta[4, z, q] == ((-((2 I Sqrt[Pi])/Sqrt[q - 1])) E^((Pi^2 + 4 z^2)/(4 Log[q])) Sum[Binomial[k + 1/2, k] Sum[(((-1)^j Binomial[k, j])/(2 j + 1)) Subscript[p, j, k] (q - 1)^k Sum[E^((m (m + 1) Pi^2)/Log[q]) Cosh[((2 m + 1) Pi z)/Log[q]], {m, 0, Infinity}], {j, 0, k}], {k, 0, Infinity}])/ E^(I Pi Floor[-(Arg[q - 1]/(2 Pi))]) /; (Abs[q] < 1 && Abs[q - 1] < 1) && Subscript[c, k] == (-1)^(k - 1)/(k + 1) && Subscript[p, j, 0] == 1 && Subscript[p, j, k] == (-(1/k)) Sum[(j m - k + m) Subscript[c, m] Subscript[p, j, k - m], {m, 1, k}] && Element[k, Integers] && k > 0

 Standard Form

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 MathML Form

 ϑ 4 ( z , q ) - 2 π q - 1 - π - arg ( q - 1 ) 2 π 4 z 2 + π 2 4 log ( q ) k = 0 ( k + 1 2 k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["k", "+", FractionBox["1", "2"]]], Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] j = 0 k ( - 1 ) j 2 j + 1 ( k j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity, Rule[Editable, True]]], List[TagBox["j", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] p j , k ( q - 1 ) k m = 0 m ( m + 1 ) π 2 log ( q ) cosh ( ( 2 m + 1 ) π z log ( q ) ) /; ( "\[LeftBracketingBar]" q "\[RightBracketingBar]" < 1 "\[LeftBracketingBar]" q - 1 "\[RightBracketingBar]" < 1 ) c k ( - 1 ) k - 1 k + 1 p j , 0 1 p j , k - 1 k m = 1 k ( j m - k + m ) c m p j , k - m k TagBox["\[DoubleStruckCapitalN]", Function[List[], Integers]] + Condition EllipticTheta 4 z q -2 1 2 q -1 1 2 -1 -1 -1 q -1 2 -1 4 z 2 2 4 q -1 k 0 Binomial k 1 2 k j 0 k -1 j 2 j 1 -1 Binomial k j Subscript p j k q -1 k m 0 m m 1 2 q -1 2 m 1 z q -1 q 1 q -1 1 Subscript c k -1 k -1 k 1 -1 Subscript p j 0 1 Subscript p j k -1 1 k -1 m 1 k j m -1 k m Subscript c m Subscript p j k -1 m k SuperPlus [/itex]

 Rule Form

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

 2007-05-02