Integral Representation for Bessel’s Functions of the First Kind and Neumann Series

  title={Integral Representation for Bessel’s Functions of the First Kind and Neumann Series},
  author={E. D. Micheli},
  journal={Results in Mathematics},
  • E. D. Micheli
  • Published 2017
  • Mathematics, Physics
  • Results in Mathematics
A Fourier-type integral representation for Bessel’s functions of the first kind and complex order is obtained by using the Gegenbauer extension of Poisson’s integral representation for the Bessel function along with a suitable trigonometric integral representation of Gegenbauer’s polynomials. By using this representation, expansions in series of Bessel’s functions of various functions which are related to the incomplete gamma function can be obtained in a unified way. Neumann series are then… Expand

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