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http://functions.wolfram.com/05.01.06.0020.01
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HermiteH[n, z] \[Proportional] ((((-1)^Floor[n/2] 2^n)/Sqrt[Pi]) E^(z^2/2)
Floor[n/2]! (Cos[((1 - (-1)^n) Pi)/4 - 2 z Sqrt[(2 n + 1)/4]] +
Sum[(Sum[((-1)^(j + r + s) 2^(2 j - 2 k + s) (1 - (-1)^n/2)^s
z^(2 (-j + k - 2 r - s)) Subscript[A, 2 (k - j - r - s)]
Cos[Pi (((-1)^n - 1)/4 + j - k + r + s) + 2 z Sqrt[(2 n + 1)/4]]
NorlundB[j, 1 - (-1)^n/2, 1 - (-1)^n/2] Pochhammer[(-1)^n/2, j]
Pochhammer[(1 - (-1)^n)/4 - j + k - s, s] Pochhammer[
(1 - (-1)^n)/4 - j + k - r - s, r] Pochhammer[(3 - (-1)^n)/4 -
j + k - r - s, r] Pochhammer[(1 + (-1)^n)/4 + j - k + r + s, r]
Pochhammer[(3 + (-1)^n)/4 + j - k + r + s, r])/
(j! s! Pochhammer[1/2, r]), {j, 0, k}, {r, 0, k - j},
{s, 0, k - j - r}] - (2/z^2) Sum[((-1)^(j + r + s) 2^(2 j - 2 k + s)
(1 - (-1)^n/2)^s z^(2 (-j + k - 2 r - s)) Subscript[A,
2 (k - j - r - s) - 1] NorlundB[j, 1 - (-1)^n/2, 1 - (-1)^n/2]
Pochhammer[(-1)^n/2, j] Pochhammer[(1 - (-1)^n)/4 - j + k - s, s]
Pochhammer[(1 - (-1)^n)/4 - j + k - r - s, r]
Pochhammer[(3 - (-1)^n)/4 - j + k - r - s, r]
Pochhammer[((-1)^n + 1)/4 + j - k + r + s, 1 + r]
Pochhammer[(3 + (-1)^n)/4 + j - k + r + s, 1 + r]
Sin[Pi (((-1)^n + 1)/4 + j - k + r + s) + 2 z Sqrt[(2 n + 1)/4]])/
(j! s! Pochhammer[3/2, r]), {j, 0, k - 1}, {r, 0, k - j - 1},
{s, 0, k - j - r - 1}])/Floor[n/2]^k, {k, 1, Infinity}] +
(z/(2 Sqrt[Floor[n/2]])) Sum[((((-1)^(j + r + s) 2^(2 j - 2 k + s))/
(j! s! Pochhammer[3/2, r])) (1 - (-1)^n/2)^s
z^(2 (k - j - 2 r - s)) NorlundB[j, 1 - (-1)^n/2, 1 - (-1)^n/2]
Pochhammer[(-1)^n/2, j] Pochhammer[(3 - (-1)^n)/4 - j + k - s, s]
Pochhammer[(3 - (-1)^n)/4 - j + k - r - s, r]
Pochhammer[(5 - (-1)^n)/4 - j + k - r - s, r]
Pochhammer[((-1)^n - 1)/4 + j - k + r + s, r]
Pochhammer[((-1)^n + 1)/4 + j - k + r + s, r]
((1 + 2 r) Subscript[A, 2 (k - j - r - s) + 1]
Cos[Pi (((-1)^n - 3)/4 + j - k + r + s) + 2 z Sqrt[(2 n + 1)/4]] -
(1/(8 z^2)) ((-1 + (-1)^n + 4 j - 4 k + 8 r + 4 s)
(1 + (-1)^n + 4 j - 4 k + 8 r + 4 s)) Subscript[A,
2 (k - j - r - s)] Sin[Pi (((-1)^n - 1)/4 + j - k + r + s) +
2 z Sqrt[(2 n + 1)/4]]))/Floor[n/2]^k, {k, 0, Infinity},
{j, 0, k}, {r, 0, k - j}, {s, 0, k - j - r}]))/
Floor[n/2]^((1 + (-1)^n)/4) /; (n -> Infinity) && Subscript[A, 0] == 1 &&
Subscript[A, 1] == 0 && Subscript[A, 2] == ((-1)^(n - 1) + 2)/4 &&
Subscript[A, m] == ((2 m + (-1)^(n - 1) - 2)/(2 m)) Subscript[A, m - 2] -
(1/2) (4 Floor[n/2] + (-1)^(n - 1) + 2) Subscript[A, m - 3] &&
Element[m, Integers] && m > 0
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RowBox[List[SubscriptBox["A", "2"], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["n", "-", "1"]]], "+", "2"]], "4"]]], "\[And]", RowBox[List[SubscriptBox["A", "m"], "\[Equal]", RowBox[List[RowBox[List[FractionBox[RowBox[List["(", RowBox[List[RowBox[List["2", "m"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["n", "-", "1"]]], "-", "2"]], ")"]], RowBox[List["2", "m"]]], " ", SubscriptBox["A", RowBox[List["m", "-", "2"]]]]], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["n", "-", "1"]]], "+", "2"]], ")"]], " ", SubscriptBox["A", RowBox[List["m", "-", "3"]]]]]]]]], "\[And]", RowBox[List["Element", "[", RowBox[List["m", ",", "Integers"]], "]"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]
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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> <msub> <mi> H </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </msup> <mo> ⁢ </mo> <msup> <mn> 2 </mn> <mi> n </mi> </msup> </mrow> <msqrt> <mi> π </mi> </msqrt> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 2 </mn> </mfrac> </msup> <mo> ⁢ </mo> <mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ⌊ </mo> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mn> 4 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <msqrt> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <msup> <mrow> <mo> ⌊ </mo> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> k </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> r </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> </mrow> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> <mo> - </mo> <mi> r </mi> </mrow> </munderover> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> j </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mn> 2 </mn> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mi> s </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> s </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "r"], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> s </mi> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msub> <mi> A </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msub> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", NorlundB] </annotation> </semantics> <mi> j </mi> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> j </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], "2"], ")"]], "j"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> s </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "-", "j", "+", "k", "-", "s"]], ")"]], "s"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "-", "j", "+", "k", "-", "r", "-", "s"]], ")"]], "r"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "-", "j", "+", "k", "-", "r", "-", "s"]], ")"]], "r"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "+", "j", "-", "k", "+", "r", "+", "s"]], ")"]], "r"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "+", "j", "-", "k", "+", "r", "+", "s"]], ")"]], "r"], Pochhammer] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 2 </mn> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> r </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> j </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mn> 2 </mn> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mi> s </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> s </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "r"], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> s </mi> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msub> <mi> A </mi> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ⁢ </mo> <mrow> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", NorlundB] </annotation> </semantics> <mi> j </mi> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> j </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], "2"], ")"]], "j"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> s </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "-", "j", "+", "k", "-", "s"]], ")"]], "s"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "-", "j", "+", "k", "-", "r", "-", "s"]], ")"]], "r"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "-", "j", "+", "k", "-", "r", "-", "s"]], ")"]], "r"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], "+", "1"]], ")"]]]], "+", "j", "-", "k", "+", "r", "+", "s"]], ")"]], RowBox[List["r", "+", "1"]]], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "+", "j", "-", "k", "+", "r", "+", "s"]], ")"]], RowBox[List["r", "+", "1"]]], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mo> ⌊ </mo> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </msqrt> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> k </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> r </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> </mrow> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> <mo> - </mo> <mi> r </mi> </mrow> </munderover> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> j </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mn> 2 </mn> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mi> s </mi> </mrow> </msup> <mtext> </mtext> </mrow> <mrow> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> s </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "r"], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> s </mi> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ⌊ </mo> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msubsup> <semantics> <mi> B </mi> <annotation encoding='Mathematica'> TagBox["B", NorlundB] </annotation> </semantics> <mi> j </mi> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> j </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], "2"], ")"]], "j"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> s </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "-", "j", "+", "k", "-", "s"]], ")"]], "s"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "-", "j", "+", "k", "-", "r", "-", "s"]], ")"]], "r"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> j </mi> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "-", "j", "+", "k", "-", "r", "-", "s"]], ")"]], "r"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], "-", "1"]], ")"]]]], "+", "j", "-", "k", "+", "r", "+", "s"]], ")"]], "r"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], "+", "1"]], ")"]]]], "+", "j", "-", "k", "+", "r", "+", "s"]], ")"]], "r"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> A </mi> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> j </mi> </mrow> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <msub> <mi> A </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> j </mi> </mrow> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msub> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> j </mi> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mi> r </mi> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> A </mi> <mn> 0 </mn> </msub> <mo>  </mo> <mn> 1 </mn> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> A </mi> <mn> 1 </mn> </msub> <mo>  </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> A </mi> <mn> 2 </mn> </msub> <mo>  </mo> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> + </mo> <mn> 2 </mn> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> A </mi> <mi> m </mi> </msub> <mo>  </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> - </mo> <mn> 2 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> m </mi> </mrow> </mfrac> <mo> ⁢ </mo> <msub> <mi> A </mi> <mrow> <mi> m </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </mrow> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> A </mi> <mrow> <mi> m </mi> <mo> - </mo> <mn> 3 </mn> </mrow> </msub> </mrow> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> m </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> HermiteH </ci> <ci> n </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <floor /> <apply> <times /> <ci> n </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <factorial /> <apply> <floor /> <apply> <times /> <ci> n </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <floor /> <apply> <times /> <ci> n </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <cos /> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <pi /> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <power /> <apply> <floor /> <apply> <times /> <ci> n </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <apply> <plus /> <apply> <sum /> <bvar> <ci> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> </apply> </uplimit> <apply> <sum /> <bvar> <ci> r </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </uplimit> <apply> <sum /> <bvar> <ci> j </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> <apply> <plus /> <ci> j </ci> <ci> r </ci> <ci> s </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> <ci> s </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> j </ci> </apply> <apply> <factorial /> <ci> s </ci> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 1 <sep /> 2 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> s </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> A </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <cos /> <apply> <plus /> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <ci> r </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> NorlundB </ci> <ci> j </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Pochhammer </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> j </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> s </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> r </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> r </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <ci> r </ci> <ci> s </ci> </apply> <ci> r </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <ci> r </ci> <ci> s </ci> </apply> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <ci> r </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <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> k </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> j </ci> <ci> r </ci> <ci> s </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> <ci> s </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> j </ci> </apply> <apply> <factorial /> <ci> s </ci> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 3 <sep /> 2 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> s </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> A </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> NorlundB </ci> <ci> j </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Pochhammer </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> j </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> s </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> r </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> r </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <ci> r </ci> <ci> s </ci> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <ci> r </ci> <ci> s </ci> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <sin /> <apply> <plus /> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <ci> r </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <floor /> <apply> <times /> <ci> n </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 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<sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <ci> n </ci> <infinity /> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> A </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> A </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> A </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> A </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> </apply> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> A </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> -2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <floor /> <apply> <times /> <ci> n </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> A </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> -3 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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