Electrostatics and zeros of Bessel functions

[摘要] We discuss an electrostatic interpretation of the zeros of the Bessel function J(v)(z) where v is an unrestricted real variable. It is known that the zeros are real when v greater than or equal to -1 and that more and more complex zeros appear when v decreases through values less than -1. The dynamic behaviour of the zeros as time t = -v increases can be modelled by the behaviour of a suitably normalized infinite set of particles of charge +1 in the presence of a varying charge v + 1/2 at the origin. The idea for this model comes from the work of Stieltjes, who interpreted the zeros of Jacobi and other orthogonal polynomials as equilibrium positions in certain one-dimensional electrostatic problems. Similar interpretations can be given for the way in which the zeros of J(v)'(z) vary with v.

[发布日期] 1995-12-29

[效力级别]  Proceedings Paper

[关键词] Bessel functions;zeros;electrostatics