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http://functions.wolfram.com/03.08.06.0032.01
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AiryBiPrime[z] \[Proportional] AiryBiPrime[Subscript[z, 0]] +
Subscript[z, 0] AiryBi[Subscript[z, 0]] (z - Subscript[z, 0]) +
(1/2) (AiryBi[Subscript[z, 0]] + Subscript[z, 0]
AiryBiPrime[Subscript[z, 0]]) (z - Subscript[z, 0])^2 +
O[(z - Subscript[z, 0])^3]
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Cell[BoxData[RowBox[List[RowBox[List["AiryBiPrime", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List["AiryBiPrime", "[", SubscriptBox["z", "0"], "]"]], "+", RowBox[List[SubscriptBox["z", "0"], RowBox[List["AiryBi", "[", SubscriptBox["z", "0"], "]"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["AiryBi", "[", SubscriptBox["z", "0"], "]"]], "+", RowBox[List[SubscriptBox["z", "0"], RowBox[List["AiryBiPrime", "[", SubscriptBox["z", "0"], "]"]]]]]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "2"]]], " ", "+", RowBox[List["O", "[", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "3"], "]"]]]]]]]]
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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> <msup> <mi> Bi </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <msup> <mi> Bi </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mtext> </mtext> <mrow> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ⁢ </mo> <mrow> <mi> Bi </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Bi </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ⁢ </mo> <mrow> <msup> <mi> Bi </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> <mtext> </mtext> <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> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> AiryBiPrime </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> AiryBiPrime </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <ci> AiryBi </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <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> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <ci> AiryBi </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </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> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> O </ci> <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> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryBiPrime", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["AiryBiPrime", "[", SubscriptBox["zz", "0"], "]"]], "+", RowBox[List[SubscriptBox["zz", "0"], " ", RowBox[List["AiryBi", "[", SubscriptBox["zz", "0"], "]"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["AiryBi", "[", SubscriptBox["zz", "0"], "]"]], "+", RowBox[List[SubscriptBox["zz", "0"], " ", RowBox[List["AiryBiPrime", "[", SubscriptBox["zz", "0"], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "2"]]], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], "3"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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