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Zbl 0962.33005
Elbert, Árpád; Laforgia, Andrea
Further results on McMahon's asymptotic approximations. (English)
[J] J. Phys. A, Math. Gen. 33, No.36, 6333-6341 (2000). ISSN 0305-4470

New inequalities are given for positive zeros of the cylinder functions $C_\nu(x)=J_\nu(x)\cos\alpha -Y_\nu(x)\sin\alpha$, $0\le\alpha<\pi$. The inequalities are given in terms of quantities arising in the McMahon asymptotic approximation of the zeros of the cylinder function. To prove the results a Sturmian comparison theorem is derived.
[N.M.Temme (Amsterdam)]

MSC 2000:: *33C10 Cylinder functions, etc.
41A60 Asymptotic problems in approximation
30C15 Zeros of polynomials, etc. (one complex variable)

Keywords: Bessel functions; asymptotic approximation of zeros

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