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SphericalBesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Integral transforms > Fourier sin transforms





http://functions.wolfram.com/03.21.22.0002.01









  


  










Input Form





FourierSinTransform[SphericalBesselJ[\[Nu], t], t, z] == (-UnitStep[1 - z]) (1/(2 Sqrt[2] z Gamma[(3 + \[Nu])/2])) Gamma[\[Nu]/2] ((-1 + z^2) Hypergeometric2F1[(1 - \[Nu])/2, (2 + \[Nu])/2, -(1/2), z^2] + (1 - 3 z^2) Hypergeometric2F1[(1 - \[Nu])/2, (2 + \[Nu])/2, 1/2, z^2]) + UnitStep[z - 1] ((2^(-(1/2) - \[Nu]) z^(-1 - \[Nu]) Cos[(Pi \[Nu])/2] Gamma[1 + \[Nu]])/Gamma[3/2 + \[Nu]]) Hypergeometric2F1[(1 + \[Nu])/2, (2 + \[Nu])/2, 3/2 + \[Nu], 1/z^2] /; z > 0 && z != 1 && Re[\[Nu]] > -2










Standard Form





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MathML Form







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Rule Form





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





2007-05-02





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