Expansion of the confluent hypergeometric function in series of Bessel functions

  title={Expansion of the confluent hypergeometric function in series of Bessel functions},
  author={Y. Luke},
  journal={Mathematics of Computation},
  • Y. Luke
  • Published 1959
  • Mathematics
  • Mathematics of Computation
An expansion of the confluent hypergeometric functioll IP(a, c, z) in series of functions of the same kind has been given by Buchholz (1). By specializa- tion of some quantities, there is obtained an expansion in series of modified Bessel functions of the first kind, Iv(z), where v depends on the parameter a. Tricomi (2, 3) has developed two expansions of similar type where both the order and -argument of the Bessel functions depend on the parameters a and c. In the present paper, we derive an… Expand
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On the function H(m, a, x) = exp {—ix)F{m + 1 — xa, 2m + 2; 2ix)'.', in Tables of Functions and of Zeros of Functions, National Bureau of Standards
  • AMS 37,
  • 1954
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  • 1953