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math.CA2025
Uniform Asymptotic approximation and numerical evaluation of the Reverse Generalized Bessel Polynomial zeros
T. M. Dunster, Amparo Gil, Diego Ruiz-Antolin +1
Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree and real parameter . It is assumed that $-Δ_{1} n+\frac…
math.CA2024
On bounds for ratios of contiguous hypergeometric functions
Javier Segura
We review recent results on analytical properties (monotonicity and bounds) for ratios of contiguous functions of hypergeometric type. The cases of parabolic cylinder functions and…
math.CA2024
Uniform asymptotic expansions for the zeros of parabolic cylinder functions
T. M. Dunster, A. Gil, D. Ruiz-Antolin +1
The real and complex zeros of the parabolic cylinder function are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and thes…