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variants of this functions
KelvinBei




Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBei[nu,z] > Integral transforms > Mellin transforms





http://functions.wolfram.com/03.17.22.0002.01









  


  








Input Form





MellinTransform[KelvinBei[\[Nu], t]/E^(p t), t, z] == (1/Gamma[1 + \[Nu]]) 2^(-2 - \[Nu]) p^(-z - \[Nu]) Gamma[z + \[Nu]] ((1/(p^2 (1 + \[Nu]))) (z + \[Nu]) (1 + z + \[Nu]) Cos[(3 Pi \[Nu])/4] HypergeometricPFQ[{(2 + z + \[Nu])/4, (3 + z + \[Nu])/4, 1 + (z + \[Nu])/4, (5 + z + \[Nu])/4}, {3/2, 1 + \[Nu]/2, (3 + \[Nu])/2}, -(1/p^4)] + 4 Sin[(3 Pi \[Nu])/4] HypergeometricPFQ[{(z + \[Nu])/4, (1 + z + \[Nu])/4, (2 + z + \[Nu])/4, (3 + z + \[Nu])/4}, {1/2, (1 + \[Nu])/2, 1 + \[Nu]/2}, -(1/p^4)]) /; Re[z + \[Nu]] > 0 && Re[p] > 1/Sqrt[2]








Standard Form





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MathML Form







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</ci> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <apply> <real /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </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