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Approximation of analytic functions by bessel functions of fractional order

We solve the inhomogeneous Bessel differential equation

$$ {x^2}y''(x) + xy'(x) + \left( {{x^2} - {\nu^2}} \right)y(x) = \sum\limits_{m = 0}^\infty {{a_m}{x^m},} $$

where ν is a positive nonintegral number, and use this result for the approximation of analytic functions of a special type by the Bessel functions of fractional order.

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Author information

Correspondence to S.-M. Jung.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 12, pp. 1699–1709, December, 2011.

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Jung, S. Approximation of analytic functions by bessel functions of fractional order. Ukr Math J 63, 1933–1944 (2012). https://doi.org/10.1007/s11253-012-0622-4

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Keywords

  • Functional Equation
  • Bessel Function
  • Fractional Order
  • Differential Inequality
  • Linear Differential Operator