Derivative of the Airy function Bi: Representations through more general functions (formula 03.08.26.0016)

AiryBiPrime

$Mathematica Notation$

Bessel-Type Functions

AiryBiPrime[z]

Representations through more general functions

Through Meijer G

Generalized cases involving Bessel I

http://functions.wolfram.com/03.08.26.0016.01

Input Form

AiryBiPrime[z] BesselI[\[Nu], (2 z^(3/2))/3] == (2^(1/3) 3^(1/6) Sqrt[Pi] (z^(3/2))^\[Nu] MeijerG[{{1/3, 5/6}, {(2 + 3 \[Nu])/6, 5/6 + \[Nu]/2}}, {{\[Nu]/2, (4 + 3 \[Nu])/6}, {-(\[Nu]/2), (4 - 3 \[Nu])/6, (2 + 3 \[Nu])/6, (5 + 3 \[Nu])/6}}, (2/3)^(2/3) z, 1/3])/z^((3 \[Nu])/2)

Standard Form

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MathML Form

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</mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 6 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mi> ν </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 5 </mn> <mn> 6 </mn> </mfrac> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> 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<apply> <times /> <apply> <ci> AiryBiPrime </ci> <ci> z </ci> </apply> <apply> <ci> BesselI </ci> <ci> ν </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <ci> ν </ci> </apply> <apply> 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Rule Form

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

2001-10-29