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JacobiDN






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiDN[z,m] > Identities involving the group of functions > Local identities of rank 4 > Rank 4 identities with 2 distinct arguments





http://functions.wolfram.com/09.29.18.0133.01









  


  










Input Form





m JacobiDN[z, m] JacobiCN[z, m] JacobiDN[z + a, m] JacobiSN[z + a, m] == JacobiDS[a, m] (JacobiCS[a, m]^2 + JacobiNS[a, m]^2) JacobiDN[z, m] - JacobiNS[a, m] (JacobiCS[a, m]^2 + JacobiDS[a, m]^2) JacobiDN[z + a, m] - m JacobiCS[a, m] JacobiDS[a, m] JacobiSN[z + a, m] JacobiCN[z + a, m] - m JacobiCS[a, m] JacobiNS[a, m] JacobiCN[z, m] JacobiSN[z, m]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["m_", " ", RowBox[List["JacobiDN", "[", RowBox[List["z_", ",", "m_"]], "]"]], " ", RowBox[List["JacobiCN", "[", RowBox[List["z_", ",", "m_"]], "]"]], " ", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z_", "+", "a_"]], ",", "m_"]], "]"]], " ", RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List["z_", "+", "a_"]], ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["JacobiDS", "[", RowBox[List["a", ",", "m"]], "]"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["JacobiCS", "[", RowBox[List["a", ",", "m"]], "]"]], "2"], "+", SuperscriptBox[RowBox[List["JacobiNS", "[", RowBox[List["a", ",", "m"]], "]"]], "2"]]], ")"]], " ", RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]]]], "-", RowBox[List[RowBox[List["JacobiNS", "[", RowBox[List["a", ",", "m"]], "]"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["JacobiCS", "[", RowBox[List["a", ",", "m"]], "]"]], "2"], "+", SuperscriptBox[RowBox[List["JacobiDS", "[", RowBox[List["a", ",", "m"]], "]"]], "2"]]], ")"]], " ", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z", "+", "a"]], ",", "m"]], "]"]]]], "-", RowBox[List["m", " ", RowBox[List["JacobiCS", "[", RowBox[List["a", ",", "m"]], "]"]], " ", RowBox[List["JacobiDS", "[", RowBox[List["a", ",", "m"]], "]"]], " ", RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List["z", "+", "a"]], ",", "m"]], "]"]], " ", RowBox[List["JacobiCN", "[", RowBox[List[RowBox[List["z", "+", "a"]], ",", "m"]], "]"]]]], "-", RowBox[List["m", " ", RowBox[List["JacobiCS", "[", RowBox[List["a", ",", "m"]], "]"]], " ", RowBox[List["JacobiNS", "[", RowBox[List["a", ",", "m"]], "]"]], " ", RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]], " ", RowBox[List["JacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]]]










References





A. Khare, A. Lakshminarayan, U. Sukhatme, "Local Identities Involving Jacobi Elliptic Functions", math-ph/0306028, (2003) http://arXiv.org/abs/math-ph/0306028










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





2003-08-21