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http://functions.wolfram.com/09.29.16.0065.01
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Sum[(-1)^k JacobiDN[z + (2 k EllipticK[m])/p, m]
JacobiDN[z + (2 (k + Subscript[n, 1]) EllipticK[m])/p, m]
JacobiDN[z + (2 (k + Subscript[n, 2]) EllipticK[m])/p, m],
{k, 0, p - 1}]/Sum[(-1)^k JacobiDN[z + (2 k EllipticK[m])/p, m],
{k, 0, p - 1}] == Sum[(-1)^k JacobiDN[(2 k EllipticK[m])/p, m]
JacobiDN[(2 (k + Subscript[n, 1]) EllipticK[m])/p, m]
JacobiDN[(2 (k + Subscript[n, 2]) EllipticK[m])/p, m], {k, 0, p - 1}]/
Sum[(-1)^k JacobiDN[(2 k EllipticK[m])/p, m], {k, 0, p - 1}] /;
Element[p/2, Integers] && p >= 2 && Element[Subscript[n, 1], Integers] &&
Element[Subscript[n, 2], Integers] && Inequality[1, LessEqual,
Subscript[n, 1], Less, Subscript[n, 2], Less, p]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p", "-", "1"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z", "+", FractionBox[RowBox[List["2", "k", " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"]]], ",", "m"]], "]"]], RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z", "+", FractionBox[RowBox[List["2", RowBox[List["(", RowBox[List["k", "+", SubscriptBox["n", "1"]]], ")"]], " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"]]], ",", "m"]], "]"]], RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z", "+", FractionBox[RowBox[List["2", RowBox[List["(", RowBox[List["k", "+", SubscriptBox["n", "2"]]], ")"]], " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"]]], ",", "m"]], "]"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p", "-", "1"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z", "+", FractionBox[RowBox[List["2", "k", " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"]]], ",", "m"]], "]"]]]]]], ")"]]]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p", "-", "1"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], RowBox[List["JacobiDN", "[", RowBox[List[FractionBox[RowBox[List["2", "k", " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"], ",", "m"]], "]"]], RowBox[List["JacobiDN", "[", RowBox[List[FractionBox[RowBox[List["2", RowBox[List["(", RowBox[List["k", "+", SubscriptBox["n", "1"]]], ")"]], " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"], ",", "m"]], "]"]], RowBox[List["JacobiDN", "[", RowBox[List[FractionBox[RowBox[List["2", RowBox[List["(", RowBox[List["k", "+", SubscriptBox["n", "2"]]], ")"]], " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"], ",", "m"]], "]"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p", "-", "1"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], RowBox[List["JacobiDN", "[", RowBox[List[FractionBox[RowBox[List["2", "k", " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"], ",", "m"]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List[FractionBox["p", "2"], "\[Element]", "Integers"]], "\[And]", RowBox[List["p", "\[GreaterEqual]", "2"]], "\[And]", RowBox[List[SubscriptBox["n", "1"], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["n", "2"], "\[Element]", "Integers"]], "\[And]", RowBox[List["1", "\[LessEqual]", SubscriptBox["n", "1"], "<", SubscriptBox["n", "2"], "<", "p"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mi> p </mi> </mfrac> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <msub> <mi> n </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> p </mi> </mfrac> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> p </mi> </mfrac> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mi> p </mi> </mfrac> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> ⩵ </mo> <mfrac> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mi> p </mi> </mfrac> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <msub> <mi> n </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mi> p </mi> </mfrac> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mi> p </mi> </mfrac> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mi> p </mi> </mfrac> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mrow> <mfrac> <mi> p </mi> <mn> 2 </mn> </mfrac> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> < </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> < </mo> <mi> p </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <ci> JacobiDN </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiDN </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <plus /> <ci> k </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiDN </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <plus /> <ci> k </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> m </ci> </apply> </apply> </apply> <apply> <power /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <ci> JacobiDN </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> m </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <ci> JacobiDN </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiDN </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> k </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiDN </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> k </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> </apply> </apply> <apply> <power /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <ci> JacobiDN </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <times /> <ci> p </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <integers /> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <integers /> </apply> <apply> <ci> Inequality </ci> <cn type='integer'> 1 </cn> <leq /> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <lt /> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <lt /> <ci> p </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p_", "-", "1"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z_", "+", FractionBox[RowBox[List["2", " ", "k", " ", RowBox[List["EllipticK", "[", "m_", "]"]]]], "p_"]]], ",", "m_"]], "]"]], " ", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z_", "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["k", "+", SubscriptBox["n_", "1"]]], ")"]], " ", RowBox[List["EllipticK", "[", "m_", "]"]]]], "p_"]]], ",", "m_"]], "]"]], " ", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z_", "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["k", "+", SubscriptBox["n_", "2"]]], ")"]], " ", RowBox[List["EllipticK", "[", "m_", "]"]]]], "p_"]]], ",", "m_"]], "]"]]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p_", "-", "1"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z_", "+", FractionBox[RowBox[List["2", " ", "k", " ", RowBox[List["EllipticK", "[", "m_", "]"]]]], "p_"]]], ",", "m_"]], "]"]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p", "-", "1"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["JacobiDN", "[", RowBox[List[FractionBox[RowBox[List["2", " ", "k", " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"], ",", "m"]], "]"]], " ", RowBox[List["JacobiDN", "[", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["k", "+", SubscriptBox["nn", "1"]]], ")"]], " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"], ",", "m"]], "]"]], " ", RowBox[List["JacobiDN", "[", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["k", "+", SubscriptBox["nn", "2"]]], ")"]], " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"], ",", "m"]], "]"]]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p", "-", "1"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["JacobiDN", "[", RowBox[List[FractionBox[RowBox[List["2", " ", "k", " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "p"], ",", "m"]], "]"]]]]]]], "/;", RowBox[List[RowBox[List[FractionBox["p", "2"], "\[Element]", "Integers"]], "&&", RowBox[List["p", "\[GreaterEqual]", "2"]], "&&", RowBox[List[SubscriptBox["nn", "1"], "\[Element]", "Integers"]], "&&", RowBox[List[SubscriptBox["nn", "2"], "\[Element]", "Integers"]], "&&", RowBox[List["1", "\[LessEqual]", SubscriptBox["nn", "1"], "<", SubscriptBox["nn", "2"], "<", "p"]]]]]]]]]] |
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| A. Khare, U. Sukhatme, "Cyclic Identities Involving Jacobi Elliptic Functions", math-ph/0201004, (2002) http://arXiv.org/abs/math-ph/0201004 A. Khare, U. Sukhatme, "Cyclic Identities Involving Jacobi Elliptic Functions", Journal of Mathematical Physics, v. 43, issue 7, pp. 3798-3806 (2002) |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
