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On the exceptional zeros of cross-products of derivatives of spherical Bessel functions. (English) Zbl 0588.33005

The author obtains an asymptotic expansion for the lowest exceptional root of the equation

j ' ν (x)y ' ν (ρx)-j ' ν (ρx)y ' ν (x)

where ' =d/dx and j ν and y ν denote the spherical Bessel functions of the first and secind kind, respectively. The result is valid for ρ 1, and it can be thought of as complementing that given by McMahon which is useful for larger zeros.

Reviewer: A.Laforgia
MSC:
33C10Bessel and Airy functions, cylinder functions, 0 F 1
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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