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 MathieuC

 http://functions.wolfram.com/11.01.06.0001.01

 Input Form

 MathieuC[MathieuCharacteristicA[2 n, q], q, z] == Sum[Subscript[A, 2 k]^(2 n) Cos[2 k z], {k, 0, Infinity}] /; MathieuCharacteristicA[2 n, q] Subscript[A, 0]^(2 n) - q Subscript[A, 2]^(2 n) == 0 && (MathieuCharacteristicA[2 n, q] - 4) Subscript[A, 2]^(2 n) - q (Subscript[A, 4]^(2 n) - 2 Subscript[A, 0]^(2 n)) == 0 && (MathieuCharacteristicA[2 n, q] - 4 k^2) Subscript[A, 2 k]^(2 n) - q (Subscript[A, 2 k + 2]^(2 n) + Subscript[A, 2 k - 2]^(2 n)) == 0 && 2 (Subscript[A, 0]^(2 n))^2 + Sum[Subscript[A, 2 k]^(2 n), {k, 1, Infinity}] == 1 && Element[n, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MathieuC", "[", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List[RowBox[List["2", "n"]], ",", "q"]], "]"]], ",", "q", ",", "z"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SubsuperscriptBox["A", RowBox[List[" ", RowBox[List["2", " ", "k"]]]], RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]], RowBox[List["Cos", "[", RowBox[List["2", "k", " ", "z"]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List[RowBox[List["2", "n"]], ",", "q"]], "]"]], SubsuperscriptBox["A", RowBox[List[" ", "0"]], RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]]]], "-", RowBox[List["q", " ", SubsuperscriptBox["A", RowBox[List[" ", "2"]], RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]]]]]], "\[Equal]", "0"]], "\[And]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List[RowBox[List["2", "n"]], ",", "q"]], "]"]], "-", "4"]], ")"]], SubsuperscriptBox["A", RowBox[List[" ", "2"]], RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]]]], "-", RowBox[List["q", RowBox[List["(", " ", RowBox[List[SubsuperscriptBox["A", RowBox[List[" ", "4"]], RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]], "-", RowBox[List["2", SubsuperscriptBox["A", RowBox[List[" ", "0"]], RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]]]]]], ")"]]]]]], "\[Equal]", "0"]], "\[And]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List[RowBox[List["2", "n"]], ",", "q"]], "]"]], "-", RowBox[List["4", SuperscriptBox["k", "2"]]]]], ")"]], SubsuperscriptBox["A", RowBox[List[" ", RowBox[List["2", "k"]]]], RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]]]], "-", RowBox[List["q", RowBox[List["(", " ", RowBox[List[SubsuperscriptBox["A", RowBox[List[" ", RowBox[List[RowBox[List["2", "k"]], "+", "2"]]]], RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]], "+", SubsuperscriptBox["A", RowBox[List[" ", RowBox[List[RowBox[List["2", "k"]], "-", "2"]]]], RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]]]], ")"]]]]]], "\[Equal]", "0"]], "\[And]", RowBox[List[RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", SubsuperscriptBox["A", "0", RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]], ")"]], "2"]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SubsuperscriptBox["A", RowBox[List["2", " ", "k"]], RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]]]]]]], "\[Equal]", "1"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

 MathML Form

 Ce ( a MathieuCharacteristicA 2 n ( q ) , q , z ) k = 0 A 2 k 2 n cos ( 2 k z ) /; a MathieuCharacteristicA 2 n ( q ) A 0 2 n - q A 2 2 n 0 ( a MathieuCharacteristicA 2 n ( q ) - 4 ) A 2 2 n - q ( A 4 2 n - 2 A 0 2 n ) 0 ( a MathieuCharacteristicA 2 n ( q ) - 4 k 2 ) A 2 k 2 n - q ( A 2 k - 2 2 n + A 2 k + 2 2 n ) 0 2 ( A 0 2 n ) 2 + k = 1 A 2 k 2 n 1 n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition Ce MathieuCharacteristicA 2 n q q z k 0 Subscript A 2 k 2 n 2 k z MathieuCharacteristicA 2 n q Subscript A 0 2 n -1 q Subscript A 2 2 n 0 MathieuCharacteristicA 2 n q -4 Subscript A 2 2 n -1 q Subscript A 4 2 n -1 2 Subscript A 0 2 n 0 MathieuCharacteristicA 2 n q -1 4 k 2 Subscript A 2 k 2 n -1 q Subscript A 2 k -2 2 n Subscript A 2 k 2 2 n 0 2 Subscript A 0 2 n 2 k 1 Subscript A 2 k 2 n 1 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MathieuC", "[", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List[RowBox[List["2", " ", "n_"]], ",", "q_"]], "]"]], ",", "q_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SubsuperscriptBox["A", RowBox[List["2", " ", "k"]], RowBox[List["2", " ", "n"]]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "k", " ", "z"]], "]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List[RowBox[List["2", " ", "n"]], ",", "q"]], "]"]], " ", SubsuperscriptBox["A", "0", RowBox[List["2", " ", "n"]]]]], "-", RowBox[List["q", " ", SubsuperscriptBox["A", "2", RowBox[List["2", " ", "n"]]]]]]], "\[Equal]", "0"]], "&&", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List[RowBox[List["2", " ", "n"]], ",", "q"]], "]"]], "-", "4"]], ")"]], " ", SubsuperscriptBox["A", "2", RowBox[List["2", " ", "n"]]]]], "-", RowBox[List["q", " ", RowBox[List["(", RowBox[List[SubsuperscriptBox["A", "4", RowBox[List["2", " ", "n"]]], "-", RowBox[List["2", " ", SubsuperscriptBox["A", "0", RowBox[List["2", " ", "n"]]]]]]], ")"]]]]]], "\[Equal]", "0"]], "&&", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List[RowBox[List["2", " ", "n"]], ",", "q"]], "]"]], "-", RowBox[List["4", " ", SuperscriptBox["k", "2"]]]]], ")"]], " ", SubsuperscriptBox["A", RowBox[List["2", " ", "k"]], RowBox[List["2", " ", "n"]]]]], "-", RowBox[List["q", " ", RowBox[List["(", RowBox[List[SubsuperscriptBox["A", RowBox[List[RowBox[List["2", " ", "k"]], "+", "2"]], RowBox[List["2", " ", "n"]]], "+", SubsuperscriptBox["A", RowBox[List[RowBox[List["2", " ", "k"]], "-", "2"]], RowBox[List["2", " ", "n"]]]]], ")"]]]]]], "\[Equal]", "0"]], "&&", RowBox[List[RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", SubsuperscriptBox["A", "0", RowBox[List["2", " ", "n"]]], ")"]], "2"]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SubsuperscriptBox["A", RowBox[List["2", " ", "k"]], RowBox[List["2", " ", "n"]]]]]]], "\[Equal]", "1"]], "&&", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]]]

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

 2001-10-29