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BesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselJ[nu,z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/03.01.21.0082.01









  


  










Input Form





Integrate[BesselJ[\[Mu], a t] BesselJ[\[Nu], b t], {t, 0, Infinity}] == Piecewise[{{(a^\[Mu] b^(-1 - \[Mu]) Gamma[(1/2) (1 + \[Mu] + \[Nu])] Hypergeometric2F1[(1/2) (1 + \[Mu] + \[Nu]), (1/2) (1 + \[Mu] - \[Nu]), 1 + \[Mu], a^2/b^2])/ (Gamma[1 + \[Mu]] Gamma[1 + (1/2) (-1 - \[Mu] + \[Nu])]), b > a}, {(a^(-1 - \[Nu]) b^\[Nu] Gamma[(1/2) (1 + \[Mu] + \[Nu])] Hypergeometric2F1[(1/2) (1 + \[Mu] + \[Nu]), (1/2) (1 - \[Mu] + \[Nu]), 1 + \[Nu], b^2/a^2])/ (Gamma[1 + (1/2) (-1 + \[Mu] - \[Nu])] Gamma[1 + \[Nu]]), a > b}}, Integrate[BesselJ[\[Mu], a t] BesselJ[\[Nu], b t], {t, 0, Infinity}]] /; a > 0 && b > 0 && Re[\[Mu] + \[Nu]] > -1










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





© 1998- Wolfram Research, Inc.