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http://functions.wolfram.com/03.07.06.0047.01
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AiryAiPrime[z] \[Proportional] (-(1/(2 Sqrt[6 Pi] (-z^3)^(7/12))))
((((-1 + Sqrt[3]) z^2 + (1 + Sqrt[3]) (-z^3)^(2/3)) Cosh[(2 z^(3/2))/3] -
Sqrt[z] (-z^3)^(1/6) ((1 - Sqrt[3]) z + (1 + Sqrt[3]) (-z^3)^(1/3))
Sinh[(2 z^(3/2))/3])
(Sum[((Pochhammer[-(1/12), k] Pochhammer[5/12, k] Pochhammer[7/12, k]
Pochhammer[13/12, k])/(Pochhammer[1/2, k] k!)) (9/(4 z^3))^k,
{k, 0, n}] + O[1/z^(3 n + 3)]) - (7/(48 (-z^3)^(1/2)))
(((1 + Sqrt[3]) z^2 + (-1 + Sqrt[3]) (-z^3)^(2/3)) Cosh[(2 z^(3/2))/3] +
Sqrt[z] (-z^3)^(1/6) ((-(1 + Sqrt[3])) z + (-1 + Sqrt[3]) (-z^3)^(1/3))
Sinh[(2 z^(3/2))/3])
(Sum[((Pochhammer[5/12, k] Pochhammer[11/12, k] Pochhammer[13/12, k]
Pochhammer[19/12, k])/(k! Pochhammer[3/2, k])) (9/(4 z^3))^k,
{k, 0, n}] + O[1/z^(3 n + 3)])) /; (Abs[z] -> Infinity) &&
Element[n, Integers] && n >= 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> <msup> <mi> Ai </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </msqrt> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 12 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mroot> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 6 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mroot> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 3 </mn> </mroot> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["1", "12"]]], ")"]], "k"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 5 </mn> <mn> 12 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["5", "12"], ")"]], "k"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 7 </mn> <mn> 12 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["7", "12"], ")"]], "k"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 13 </mn> <mn> 12 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["13", "12"], ")"]], "k"], Pochhammer] </annotation> </semantics> </mrow> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "k"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mn> 9 </mn> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msup> </mrow> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> </msup> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 7 </mn> <mrow> <mn> 48 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mroot> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 6 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mroot> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mn> 3 </mn> </mroot> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 5 </mn> <mn> 12 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["5", "12"], ")"]], "k"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 11 </mn> <mn> 12 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["11", "12"], ")"]], "k"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 13 </mn> <mn> 12 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["13", "12"], ")"]], "k"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 19 </mn> <mn> 12 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["19", "12"], ")"]], "k"], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "k"], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mn> 9 </mn> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msup> </mrow> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> </msup> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∧ </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> AiryAiPrime </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 6 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 7 <sep /> 12 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <ci> Pochhammer </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 12 </cn> </apply> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 5 <sep /> 12 </cn> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 7 <sep /> 12 </cn> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 13 <sep /> 12 </cn> <ci> k </ci> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Pochhammer </ci> <cn type='rational'> 1 <sep /> 2 </cn> <ci> k </ci> </apply> <apply> <factorial /> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> k </ci> </apply> </apply> </apply> <apply> <ci> O </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> n </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 48 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <ci> Pochhammer </ci> <cn type='rational'> 5 <sep /> 12 </cn> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 11 <sep /> 12 </cn> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 13 <sep /> 12 </cn> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 19 <sep /> 12 </cn> <ci> k </ci> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 3 <sep /> 2 </cn> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> k </ci> </apply> </apply> </apply> <apply> <ci> O </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> n </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <apply> <abs /> <ci> z </ci> </apply> <infinity /> </apply> <apply> <in /> <ci> n </ci> <ci> ℕ </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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