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AiryAiPrime






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.07.16.0001.01









  


  










Input Form





AiryAiPrime[c (d z^n)^m] == (1/2) ((d z^3)^(2 m)/(d^(2 m) z^(6 m)) + 1) AiryAiPrime[c d^m z^(3 m)] - ((1 - (d z^3)^(2 m)/(d^(2 m) z^(6 m))) AiryBiPrime[c d^m z^(3 m)])/(2 Sqrt[3]) /; IntegerQ[3 m]










Standard Form





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MathML Form







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</mo> </msup> <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> <mn> 3 </mn> <mo> &#8290; </mo> <mi> m </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> IntegerQ </mi> <mo> [ </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> ] </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> AiryAiPrime </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> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 6 </cn> <ci> m </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> AiryAiPrime </ci> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> d </ci> <ci> m </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> m </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 /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <times /> <ci> d </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 6 </cn> <ci> m </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> AiryBiPrime </ci> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> d </ci> <ci> m </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> IntegerQ </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> m </ci> </apply> </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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