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AiryAi






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryAi[z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/03.05.16.0001.01









  


  










Input Form





AiryAi[c (d z^n)^m] == (1/2) ((d z^n)^m/(d^m z^(m n)) + 1) AiryAi[c d^m z^(m n)] - (1/(2 Sqrt[3])) ((d z^n)^m/(d^m z^(m n)) - 1) AiryBi[c d^m z^(m n)] /; Element[3 m, Integers]










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> Ai </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mi> m </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mi> m </mi> </msup> <mrow> <msup> <mi> d </mi> <mi> m </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msup> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Ai </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> d </mi> <mi> m </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> n </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mi> m </mi> </msup> <mrow> <msup> <mi> d </mi> <mi> m </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msup> </mrow> </mfrac> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Bi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> d </mi> <mi> m </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> AiryAi </ci> <apply> <times /> <ci> c </ci> <apply> <power /> <apply> <times /> <ci> d </ci> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> </apply> <ci> m </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <times /> <ci> d </ci> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> </apply> <ci> m </ci> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> d </ci> <ci> m </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> AiryAi </ci> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> d </ci> <ci> m </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <times /> <ci> d </ci> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> </apply> <ci> m </ci> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> d </ci> <ci> m </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> AiryBi </ci> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> d </ci> <ci> m </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> m </ci> </apply> <ci> &#8484; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





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