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AiryBi




Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryBi[z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/03.06.06.0033.01









  


  








Input Form





AiryBi[z] == AiryBi[Subscript[z, 0]]/2 + Sum[(1/k!) ((1/(Subscript[z, 0]^k 2)) (Sum[(((-1)^(j + s - 1) i (s - i - 1)! (3 s - 3 i - 1) Pochhammer[3 s - 3 j - k + 1, k] Pochhammer[-(1/3), s])/ (i! j! (s - j)! (s - 2 i)! Pochhammer[2/3, i] Pochhammer[4/3 - 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 - 3 j + 3 s) Pochhammer[3 s - 3 j - k + 2, k - 1] Pochhammer[1/3, s])/ (i! j! (s - j)! (s - 2 i)! Pochhammer[1/3, i] Pochhammer[2/3 - s, i])) (-(Subscript[z, 0]^3/9))^i, {s, 0, k}, {j, 0, s}, {i, 0, s}]) AiryBi[Subscript[z, 0]] + (Subscript[z, 0]^(1 - k)/2) (Sum[(((-1)^(j + s - 1) (s - i - 1)! (1 - 3 j + 3 s) Pochhammer[3 s - 3 j - k + 2, k - 1] Pochhammer[1/3, s])/ (i! j! (s - j)! (s - 2 i - 1)! Pochhammer[4/3, i] Pochhammer[2/3 - 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[-(1/3), s])/(i! j! (s - j)! (s - 2 i - 1)! Pochhammer[2/3, i] Pochhammer[4/3 - s, i])) (-(Subscript[z, 0]^3/9))^i, {s, 0, k}, {j, 0, s}, {i, 0, s - 1}]) AiryBiPrime[Subscript[z, 0]]) (z - Subscript[z, 0])^k, {k, 0, Infinity}]








Standard Form





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MathML Form







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<mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> s </mi> </munderover> <mrow> <munderover> <mo> &#8721; </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> &#8290; </mo> <mi> i </mi> <mo> &#8290; </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> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8290; </mo> <mi> i </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> 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&quot;3&quot;]]], &quot;)&quot;]], &quot;s&quot;], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mrow> <mi> i </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> i </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </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[&quot;(&quot;, FractionBox[&quot;2&quot;, &quot;3&quot;], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 4 </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[&quot;(&quot;, RowBox[List[FractionBox[&quot;4&quot;, &quot;3&quot;], &quot;-&quot;, &quot;s&quot;]], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> &#8290; </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> &#8721; </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> k </mi> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> s </mi> </munderover> <mrow> <munderover> <mo> &#8721; </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> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mi> i </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8290; </mo> <mi> j </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8290; </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[RowBox[List[&quot;-&quot;, &quot;3&quot;]], &quot; &quot;, &quot;j&quot;]], &quot;-&quot;, &quot;k&quot;, &quot;+&quot;, RowBox[List[&quot;3&quot;, &quot; &quot;, &quot;s&quot;]], &quot;+&quot;, &quot;2&quot;]], &quot;)&quot;]], RowBox[List[&quot;k&quot;, &quot;-&quot;, &quot;1&quot;]]], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> s </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, FractionBox[&quot;1&quot;, &quot;3&quot;], &quot;)&quot;]], &quot;s&quot;], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mrow> <mi> i </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> i </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </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[&quot;(&quot;, FractionBox[&quot;1&quot;, &quot;3&quot;], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 2 </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[&quot;(&quot;, RowBox[List[FractionBox[&quot;2&quot;, &quot;3&quot;], &quot;-&quot;, &quot;s&quot;]], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> &#8290; </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> &#8290; </mo> <mrow> <mi> Bi </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mrow> <msubsup> <mi> z </mi> <mn> 0 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> k </mi> </mrow> </msubsup> <mtext> </mtext> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> k </mi> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> s </mi> </munderover> <mrow> <munderover> <mo> &#8721; </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> &#8290; </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> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8290; </mo> <mi> j </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8290; </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[RowBox[List[RowBox[List[&quot;-&quot;, &quot;3&quot;]], &quot; &quot;, &quot;j&quot;]], &quot;-&quot;, &quot;k&quot;, &quot;+&quot;, RowBox[List[&quot;3&quot;, &quot; &quot;, &quot;s&quot;]], &quot;+&quot;, &quot;2&quot;]], &quot;)&quot;]], RowBox[List[&quot;k&quot;, &quot;-&quot;, &quot;1&quot;]]], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> s </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, FractionBox[&quot;1&quot;, &quot;3&quot;], &quot;)&quot;]], &quot;s&quot;], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mrow> <mi> i </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> i </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 4 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, FractionBox[&quot;4&quot;, &quot;3&quot;], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 2 </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[&quot;(&quot;, RowBox[List[FractionBox[&quot;2&quot;, &quot;3&quot;], &quot;-&quot;, &quot;s&quot;]], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> &#8290; </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> &#8721; </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> k </mi> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> s </mi> </munderover> <mrow> <munderover> <mo> &#8721; </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> &#8290; </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> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8290; </mo> <mi> j </mi> </mrow> <mo> - </mo> <mi> k </mi> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </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[&quot;(&quot;, RowBox[List[RowBox[List[RowBox[List[&quot;-&quot;, &quot;3&quot;]], &quot; &quot;, &quot;j&quot;]], &quot;-&quot;, &quot;k&quot;, &quot;+&quot;, RowBox[List[&quot;3&quot;, &quot; &quot;, &quot;s&quot;]], &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;k&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> s </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;-&quot;, FractionBox[&quot;1&quot;, &quot;3&quot;]]], &quot;)&quot;]], &quot;s&quot;], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mrow> <mi> i </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> j </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> i </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </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[&quot;(&quot;, FractionBox[&quot;2&quot;, &quot;3&quot;], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 4 </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[&quot;(&quot;, RowBox[List[FractionBox[&quot;4&quot;, &quot;3&quot;], &quot;-&quot;, &quot;s&quot;]], &quot;)&quot;]], &quot;i&quot;], Pochhammer] </annotation> </semantics> </mrow> </mfrac> <mo> &#8290; </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> &#8290; </mo> <mrow> <msup> <mi> Bi </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </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> AiryBi </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> AiryBi </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </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'> 2 </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> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> j </ci> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> i </ci> <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'> 3 </cn> <ci> s </ci> </apply> <cn type='integer'> -1 </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'> 1 <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 /> <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'> 4 <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> <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> <cn type='integer'> -1 </cn> </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> <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'> 2 </cn> </apply> <apply> <plus /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 1 <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'> 1 <sep /> 3 </cn> <ci> i </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <cn type='rational'> 2 <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> <times /> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </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> <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> <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'> 2 </cn> </apply> <apply> <plus /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Pochhammer </ci> <cn type='rational'> 1 <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 /> <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'> 4 <sep /> 3 </cn> <ci> i </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <cn type='rational'> 2 <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'> 1 <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'> 2 <sep /> 3 </cn> <ci> i </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <cn type='rational'> 4 <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> AiryBiPrime </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>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02