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http://functions.wolfram.com/09.31.06.0006.01
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JacobiNC[z, m] == Sum[(k + 1) Sum[(((-1)^r Binomial[k, r])/(1 + r))
Subscript[p, r, k] z^(2 k), {r, 0, k}], {k, 0, Infinity}] /;
Subscript[p, j, 0] == 1 && Subscript[p, j, k] ==
(1/k) Sum[(j i - k + i) (((-1)^i Subscript[cn, i][m])/(2 i)!)
Subscript[p, j, k - i], {i, 1, k}] && Element[k, Integers] && k > 0 &&
Subscript[sn, 0][m] == 1 && Subscript[sn, n][m] ==
Sum[Binomial[2 n, 2 j] Subscript[cn, j][m] Subscript[dn, k][m]
KroneckerDelta[j + k - n], {j, 0, n}, {k, 0, n}] &&
Subscript[cn, 0][m] == 1 && Subscript[cn, n][m] ==
Sum[Binomial[2 n - 1, 2 j + 1] Subscript[sn, j][m] Subscript[dn, k][m]
KroneckerDelta[j + k - n + 1], {j, 0, n - 1}, {k, 0, n - 1}] &&
Subscript[dn, 0][m] == 1 && Subscript[dn, n][m] ==
m Sum[Binomial[2 n - 1, 2 j + 1] Subscript[sn, j][m] Subscript[cn, k][m]
KroneckerDelta[j + k - n + 1], {j, 0, n - 1}, {k, 0, n - 1}]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiNC", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["r", "=", "0"]], "k"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "r"], " ", RowBox[List["Binomial", "[", RowBox[List["k", ",", "r"]], "]"]]]], RowBox[List["1", "+", "r"]]], SubscriptBox["p", RowBox[List["r", ",", "k"]]], SuperscriptBox["z", RowBox[List["2", "k"]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["p", RowBox[List["j", ",", "0"]]], "\[Equal]", "1"]], "\[And]", RowBox[List[SubscriptBox["p", RowBox[List["j", ",", "k"]]], "\[Equal]", RowBox[List[FractionBox["1", "k"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "1"]], "k"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["j", " ", "i"]], "-", "k", "+", "i"]], ")"]], " ", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "i"], " ", RowBox[List[SubscriptBox["cn", "i"], "[", "m", "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", "i"]], ")"]], "!"]]], " ", SubscriptBox["p", RowBox[List["j", ",", RowBox[List["k", "-", "i"]]]]]]]]]]]]], "\[And]", RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", ">", "0"]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["sn", "0"], "[", "m", "]"]], "\[Equal]", "1"]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["sn", "n"], "[", "m", "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["2", " ", "n"]], ",", RowBox[List["2", " ", "j"]]]], "]"]], " ", RowBox[List[SubscriptBox["cn", "j"], "[", "m", "]"]], RowBox[List[SubscriptBox["dn", "k"], "[", "m", "]"]], RowBox[List["KroneckerDelta", "[", RowBox[List["j", "+", "k", "-", "n"]], "]"]]]]]]]]]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["cn", "0"], "[", "m", "]"]], "\[Equal]", "1"]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["cn", "n"], "[", "m", "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]], ",", RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]]], "]"]], " ", RowBox[List[SubscriptBox["sn", "j"], "[", "m", "]"]], RowBox[List[SubscriptBox["dn", "k"], "[", "m", "]"]], RowBox[List["KroneckerDelta", "[", RowBox[List["j", "+", "k", "-", "n", "+", "1"]], "]"]]]]]]]]]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["dn", "0"], "[", "m", "]"]], "\[Equal]", "1"]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["dn", "n"], "[", "m", "]"]], "\[Equal]", RowBox[List["m", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]], ",", RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]]], "]"]], " ", RowBox[List[SubscriptBox["sn", "j"], "[", "m", "]"]], RowBox[List[SubscriptBox["cn", "k"], "[", "m", "]"]], RowBox[List["KroneckerDelta", "[", RowBox[List["j", "+", "k", "-", "n", "+", "1"]], "]"]]]]]]]]]]]]]]]]]]
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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> <mrow> <mi> nc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> r </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> k </mi> </munderover> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msup> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> <mtr> <mtd> <mi> r </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity, Rule[Editable, True]]], List[TagBox["r", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> <mo> ⁢ </mo> <msub> <mi> p </mi> <mrow> <mi> r </mi> <mo> , </mo> <mi> k </mi> </mrow> </msub> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </msup> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> p </mi> <mrow> <mi> j </mi> <mo> , </mo> <mn> 0 </mn> </mrow> </msub> <mo>  </mo> <mn> 1 </mn> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> p </mi> <mrow> <mi> j </mi> <mo> , </mo> <mi> k </mi> </mrow> </msub> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> k </mi> </mfrac> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> i </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> k </mi> </munderover> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> j </mi> <mo> ⁢ </mo> <mi> i </mi> </mrow> <mo> + </mo> <mi> i </mi> <mo> - </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> cn </mi> <mi> i </mi> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> p </mi> <mrow> <mi> j </mi> <mo> , </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> i </mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> i </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> k </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <mrow> <msub> <mi> sn </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mn> 1 </mn> </mrow> <mo> ∧ </mo> <mrow> <mrow> <msub> <mi> sn </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["2", " ", "n"]], Identity, Rule[Editable, True]]], List[TagBox[RowBox[List["2", " ", "j"]], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <msub> <mi> cn </mi> <mi> j </mi> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> dn </mi> <mi> k </mi> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> n </mi> </mrow> </msub> </mrow> </mrow> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mrow> <msub> <mi> cn </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mn> 1 </mn> </mrow> <mo> ∧ </mo> <mrow> <mrow> <msub> <mi> cn </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]], Identity, Rule[Editable, True]]], List[TagBox[RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <msub> <mi> sn </mi> <mi> j </mi> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> dn </mi> <mi> k </mi> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> </mrow> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mrow> <msub> <mi> dn </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mn> 1 </mn> </mrow> <mo> ∧ </mo> <mrow> <mrow> <msub> <mi> dn </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]], Identity, Rule[Editable, True]]], List[TagBox[RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <msub> <mi> sn </mi> <mi> j </mi> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> cn </mi> <mi> k </mi> </msub> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> JacobiNC </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> <apply> <sum /> <bvar> <ci> r </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> k </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> k </ci> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> r </ci> <ci> k </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> k </ci> </uplimit> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> j </ci> <ci> i </ci> </apply> <ci> i </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <apply> <power /> <cn type='integer'> -1 </cn> <ci> i </ci> </apply> <apply> <apply> <ci> Subscript </ci> <ci> cn </ci> <ci> i </ci> </apply> <ci> m </ci> </apply> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> i </ci> </apply> </apply> </apply> <apply> <power /> <apply> <factorial /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> i </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> k </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> sn </ci> <cn type='integer'> 0 </cn> </apply> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> sn </ci> <ci> n </ci> </apply> <ci> m </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> cn </ci> <ci> j </ci> </apply> <ci> m </ci> </apply> <apply> <apply> <ci> Subscript </ci> <ci> dn </ci> <ci> k </ci> </apply> <ci> m </ci> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <plus /> <ci> j </ci> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> cn </ci> <cn type='integer'> 0 </cn> </apply> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> cn </ci> <ci> n </ci> </apply> <ci> m </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> sn </ci> <ci> j </ci> </apply> <ci> m </ci> </apply> <apply> <apply> <ci> Subscript </ci> <ci> dn </ci> <ci> k </ci> </apply> <ci> m </ci> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <plus /> <ci> j </ci> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> dn </ci> <cn type='integer'> 0 </cn> </apply> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> dn </ci> <ci> n </ci> </apply> <ci> m </ci> </apply> <apply> <times /> <ci> m </ci> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> sn </ci> <ci> j </ci> </apply> <ci> m </ci> </apply> <apply> <apply> <ci> Subscript </ci> <ci> cn </ci> <ci> k </ci> </apply> <ci> m </ci> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <plus /> <ci> j </ci> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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