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Integrals involving products of bessel functions

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Summary

The integrals\(\int\limits_0^\infty {e^{ - \lambda } \lambda ^{k - 1} K_v (\lambda )K_\mu \left( {x\lambda ^{ \pm \tfrac{1}{n}} } \right)} d\lambda \) and\(\int\limits_0^\infty {e^{ - \lambda } \lambda ^{k - 1} K_v (\lambda )J_\mu \left( {2x\lambda ^{ \pm \tfrac{1}{n}} } \right)} d\lambda \), where n is any positive integer, are evaluated in terms ofMacRobert E-functions and generalized hypergeometric functions.

References

  1. [1]

    MacRobert, T. M.,Functions of a complex Variable, (4th edit), London, (1954).

  2. [2]

    R. K. Saxena,Integrals involving E-functions, « Proc. Glasgow Math, Assoc. », Vol. (4), pag. 182 (1959).

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Ragab, F.M. Integrals involving products of bessel functions. Annali di Matematica 56, 301–311 (1961). https://doi.org/10.1007/BF02414277

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Keywords

  • Positive Integer
  • Bessel Function
  • Hypergeometric Function
  • Generalize Hypergeometric Function