|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/03.08.06.0033.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
AiryBiPrime[z] == AiryBiPrime[Subscript[z, 0]]/2 +
Sum[(1/k!) ((Subscript[z, 0]^(2 - k)/4)
(Sum[(((-1)^(j + s - 1) (s - i - 1)! (1 - 3 j + 3 s) (2 - 3 j + 3 s)
Pochhammer[3 s - 3 j - k + 3, k - 2] Pochhammer[2/3, s])/
(i! j! (s - j)! (s - 2 i - 1)! Pochhammer[5/3, i]
Pochhammer[1/3 - s, i])) (-(Subscript[z, 0]^3/9))^i, {s, 0, k},
{j, 0, s}, {i, 0, s - 1}] -
Sum[(((-1)^(j + s - 1) (s - i - 1)! Pochhammer[3 s - 3 j - k + 1, k]
Pochhammer[-(2/3), s])/(i! j! (s - j)! (s - 2 i - 1)!
Pochhammer[1/3, i] Pochhammer[5/3 - s, i]))
(-(Subscript[z, 0]^3/9))^i, {s, 0, k}, {j, 0, s}, {i, 0, s - 1}])
AiryBi[Subscript[z, 0]] + (1/(Subscript[z, 0]^k 4))
(Sum[(((-1)^(j + s) (s - i - 1)! (2 + 3 i - 3 s)
Pochhammer[3 s - 3 j - k + 1, k] Pochhammer[-(2/3), s])/
((i - 1)! j! (s - j)! (s - 2 i)! Pochhammer[1/3, i]
Pochhammer[5/3 - s, i])) (-(Subscript[z, 0]^3/9))^i, {s, 0, k},
{j, 0, s}, {i, 0, s - 1}] +
2 Sum[(((-1)^(j + s) (s - i)! (1 - 3 j + 3 s) (2 - 3 j + 3 s)
Pochhammer[3 s - 3 j - k + 3, k - 2] Pochhammer[2/3, s])/
(i! j! (s - j)! (s - 2 i)! Pochhammer[2/3, i] Pochhammer[1/3 - s,
i])) (-(Subscript[z, 0]^3/9))^i, {s, 0, k}, {j, 0, s},
{i, 0, s}]) AiryBiPrime[Subscript[z, 0]]) (z - Subscript[z, 0])^k,
{k, 0, Infinity}]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["AiryBiPrime", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["AiryBiPrime", "[", SubscriptBox["z", "0"], "]"]], "2"], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox["1", RowBox[List["k", "!"]]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox[SubsuperscriptBox["z", "0", RowBox[List["2", "-", "k"]]], "4"], RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], "k"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "s"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], RowBox[List["s", "-", "1"]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["j", "+", "s", "-", "1"]]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "i", "-", "1"]], ")"]], "!"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "j"]], "+", RowBox[List["3", " ", "s"]]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["3", " ", "j"]], "+", RowBox[List["3", " ", "s"]]]], ")"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["3", " ", "s"]], "-", RowBox[List["3", " ", "j"]], "-", "k", "+", "3"]], ",", RowBox[List["k", "-", "2"]]]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["2", "3"], ",", "s"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["i", "!"]], " ", RowBox[List["j", "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", RowBox[List["2", "i"]], "-", "1"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["5", "3"], ",", "i"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["1", "3"], "-", "s"]], ",", "i"]], "]"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SubsuperscriptBox["z", "0", "3"], "9"]]], ")"]], "i"]]]]]]]]], " ", "-", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], "k"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "s"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], RowBox[List["s", "-", "1"]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["j", "+", "s", "-", "1"]]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "i", "-", "1"]], ")"]], "!"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["3", " ", "s"]], "-", RowBox[List["3", " ", "j"]], "-", "k", "+", "1"]], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], ",", "s"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["i", "!"]], RowBox[List["j", "!"]], RowBox[List[RowBox[List["(", RowBox[List["s", "-", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", RowBox[List["2", "i"]], "-", "1"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "3"], ",", "i"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["5", "3"], "-", "s"]], ",", "i"]], "]"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SubsuperscriptBox["z", "0", "3"], "9"]]], ")"]], "i"]]]]]]]]]]], ")"]], " ", RowBox[List["AiryBi", "[", SubscriptBox["z", "0"], "]"]]]], "+", RowBox[List[FractionBox[SubsuperscriptBox["z", "0", RowBox[List["-", "k"]]], "4"], RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], "k"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "s"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], RowBox[List["s", "-", "1"]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["j", "+", "s"]]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "i", "-", "1"]], ")"]], "!"]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["3", " ", "i"]], "-", RowBox[List["3", " ", "s"]]]], ")"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["3", " ", "s"]], "-", RowBox[List["3", "j"]], "-", "k", "+", "1"]], ",", "k"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], ",", "s"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["i", "-", "1"]], ")"]], "!"]], " ", RowBox[List["j", "!"]], RowBox[List[RowBox[List["(", RowBox[List["s", "-", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", RowBox[List["2", " ", "i"]]]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "3"], ",", "i"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["5", "3"], "-", "s"]], ",", "i"]], "]"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SubsuperscriptBox["z", "0", "3"], "9"]]], ")"]], "i"]]]]]]]]], "+", RowBox[List["2", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], "k"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "s"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "s"], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["j", "+", "s"]]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "i"]], ")"]], "!"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "j"]], "+", RowBox[List["3", " ", "s"]]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["3", " ", "j"]], "+", RowBox[List["3", " ", "s"]]]], ")"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["3", " ", "s"]], "-", RowBox[List["3", " ", "j"]], "-", "k", "+", "3"]], ",", RowBox[List["k", "-", "2"]]]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["2", "3"], ",", "s"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["i", "!"]], " ", RowBox[List["j", "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", RowBox[List["2", " ", "i"]]]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["2", "3"], ",", "i"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["1", "3"], "-", "s"]], ",", "i"]], "]"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SubsuperscriptBox["z", "0", "3"], "9"]]], ")"]], "i"]]]]]]]]]]]]], ")"]], RowBox[List["AiryBiPrime", "[", SubscriptBox["z", "0"], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "k"]]]]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> Bi </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <msup> <mi> Bi </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <msubsup> <mi> z </mi> <mn> 0 </mn> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msubsup> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> k </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> s </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> i </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> s </mi> </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> s </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mi> i </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "j"]], "-", "k", "+", RowBox[List["3", " ", "s"]], "+", "3"]], ")"]], RowBox[List["k", "-", "2"]]], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> s </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], "s"], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mrow> <mi> i </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> i </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], "i"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "3"], "-", "s"]], ")"]], "i"], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 0 </mn> <mn> 3 </mn> </msubsup> <mn> 9 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msup> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> k </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> s </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> i </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> s </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> s </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> i </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> i </mi> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "j"]], "-", "k", "+", RowBox[List["3", " ", "s"]], "+", "1"]], ")"]], "k"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> s </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["2", "3"]]], ")"]], "s"], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> i </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> i </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "3"], ")"]], "i"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 3 </mn> </mfrac> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["5", "3"], "-", "s"]], ")"]], "i"], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 0 </mn> <mn> 3 </mn> </msubsup> <mn> 9 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msup> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> Bi </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <msubsup> <mi> z </mi> <mn> 0 </mn> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> k </mi> </mrow> </msubsup> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> k </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> s </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> i </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> j </mi> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> i </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "j"]], "-", "k", "+", RowBox[List["3", " ", "s"]], "+", "3"]], ")"]], RowBox[List["k", "-", "2"]]], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> s </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], "s"], Pochhammer] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> i </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> i </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 5 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["5", "3"], ")"]], "i"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "3"], "-", "s"]], ")"]], "i"], Pochhammer] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 0 </mn> <mn> 3 </mn> </msubsup> <mn> 9 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msup> </mrow> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> k </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> s </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> i </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> s </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> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> i </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "j"]], "-", "k", "+", RowBox[List["3", " ", "s"]], "+", "1"]], ")"]], "k"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> s </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["2", "3"]]], ")"]], "s"], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mrow> <mi> i </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> i </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "3"], ")"]], "i"], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 3 </mn> </mfrac> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["5", "3"], "-", "s"]], ")"]], "i"], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 0 </mn> <mn> 3 </mn> </msubsup> <mn> 9 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> i </mi> </msup> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Bi </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> AiryBiPrime </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <ci> AiryBiPrime </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> s </ci> </uplimit> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> s </ci> </uplimit> <apply> <sum /> <bvar> <ci> s </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> s </ci> </apply> </apply> <apply> <factorial /> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> i </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> s </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> s </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> k </ci> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 2 <sep /> 3 </cn> <ci> s </ci> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> i </ci> </apply> <apply> <factorial /> <ci> j </ci> </apply> <apply> <factorial /> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <factorial /> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> i </ci> </apply> </apply> </apply> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 2 <sep /> 3 </cn> <ci> i </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> i </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 9 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> i </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> s </ci> </uplimit> <apply> <sum /> <bvar> <ci> s </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> s </ci> </apply> </apply> <apply> <factorial /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> i </ci> </apply> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> i </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> s </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> s </ci> </apply> <cn type='integer'> 1 </cn> </apply> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <ci> s </ci> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <apply> <plus /> <ci> i </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <factorial /> <ci> j </ci> </apply> <apply> <factorial /> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <factorial /> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> i </ci> </apply> </apply> </apply> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 1 <sep /> 3 </cn> <ci> i </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <cn type='rational'> 5 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> i </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 9 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> i </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> AiryBiPrime </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> s </ci> </uplimit> <apply> <sum /> <bvar> <ci> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> k </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> j </ci> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <factorial /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> i </ci> </apply> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> s </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> s </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> k </ci> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 2 <sep /> 3 </cn> <ci> s </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> i </ci> </apply> <apply> <factorial /> <ci> j </ci> </apply> <apply> <factorial /> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <factorial /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> i </ci> </apply> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 5 <sep /> 3 </cn> <ci> i </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> i </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 9 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> i </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> s </ci> </uplimit> <apply> <sum /> <bvar> <ci> s </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> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <factorial /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> i </ci> </apply> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> s </ci> </apply> <cn type='integer'> 1 </cn> </apply> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <ci> s </ci> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> i </ci> </apply> <apply> <factorial /> <ci> j </ci> </apply> <apply> <factorial /> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <factorial /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> i </ci> </apply> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 1 <sep /> 3 </cn> <ci> i </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <cn type='rational'> 5 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> i </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 9 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> i </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> AiryBi </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryBiPrime", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["AiryBiPrime", "[", SubscriptBox["zz", "0"], "]"]], "2"], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", SubsuperscriptBox["zz", "0", RowBox[List["2", "-", "k"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], "k"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "s"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], RowBox[List["s", "-", "1"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["j", "+", "s", "-", "1"]]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "i", "-", "1"]], ")"]], "!"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "j"]], "+", RowBox[List["3", " ", "s"]]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["3", " ", "j"]], "+", RowBox[List["3", " ", "s"]]]], ")"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["3", " ", "s"]], "-", RowBox[List["3", " ", "j"]], "-", "k", "+", "3"]], ",", RowBox[List["k", "-", "2"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["2", "3"], ",", "s"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SubsuperscriptBox["zz", "0", "3"], "9"]]], ")"]], "i"]]], RowBox[List[RowBox[List["i", "!"]], " ", RowBox[List["j", "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", RowBox[List["2", " ", "i"]], "-", "1"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["5", "3"], ",", "i"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["1", "3"], "-", "s"]], ",", "i"]], "]"]]]]]]]]]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], "k"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "s"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], RowBox[List["s", "-", "1"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["j", "+", "s", "-", "1"]]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "i", "-", "1"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["3", " ", "s"]], "-", RowBox[List["3", " ", "j"]], "-", "k", "+", "1"]], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], ",", "s"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SubsuperscriptBox["zz", "0", "3"], "9"]]], ")"]], "i"]]], RowBox[List[RowBox[List["i", "!"]], " ", RowBox[List["j", "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", RowBox[List["2", " ", "i"]], "-", "1"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "3"], ",", "i"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["5", "3"], "-", "s"]], ",", "i"]], "]"]]]]]]]]]]]]], ")"]], " ", RowBox[List["AiryBi", "[", SubscriptBox["zz", "0"], "]"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", SubsuperscriptBox["zz", "0", RowBox[List["-", "k"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], "k"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "s"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], RowBox[List["s", "-", "1"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["j", "+", "s"]]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "i", "-", "1"]], ")"]], "!"]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["3", " ", "i"]], "-", RowBox[List["3", " ", "s"]]]], ")"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["3", " ", "s"]], "-", RowBox[List["3", " ", "j"]], "-", "k", "+", "1"]], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], ",", "s"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SubsuperscriptBox["zz", "0", "3"], "9"]]], ")"]], "i"]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["i", "-", "1"]], ")"]], "!"]], " ", RowBox[List["j", "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", RowBox[List["2", " ", "i"]]]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "3"], ",", "i"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["5", "3"], "-", "s"]], ",", "i"]], "]"]]]]]]]]]]], "+", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], "k"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "s"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "s"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["j", "+", "s"]]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "i"]], ")"]], "!"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "j"]], "+", RowBox[List["3", " ", "s"]]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["3", " ", "j"]], "+", RowBox[List["3", " ", "s"]]]], ")"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["3", " ", "s"]], "-", RowBox[List["3", " ", "j"]], "-", "k", "+", "3"]], ",", RowBox[List["k", "-", "2"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["2", "3"], ",", "s"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SubsuperscriptBox["zz", "0", "3"], "9"]]], ")"]], "i"]]], RowBox[List[RowBox[List["i", "!"]], " ", RowBox[List["j", "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["s", "-", RowBox[List["2", " ", "i"]]]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["2", "3"], ",", "i"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["1", "3"], "-", "s"]], ",", "i"]], "]"]]]]]]]]]]]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", SubscriptBox["zz", "0"], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|