Zeros of the Bessel J and Y functions and their derivatives
This package provides functions to compute the zeros of the J and Y functions, and the zeros of their derivatives, where J and Y are Bessel functions of the first and second kind, respectively.
For all functions described below, the order nu::Real is a finite number and n::Integer is a
positive integer. When nu isa AbstractFloat, the returned value has the same type as nu. When
nu isa Integer, the usual promotion rules apply, so that for most builtin integer types the output
type will be Float64. However, when nu isa BigInt the output type will be BigFloat.
When the output type is Float64, the exported functions (besselj_zero, bessely_zero,
besselj_deriv_zero, and bessely_deriv_zero) will use lookup tables to rapidly return function
zeros if the order nu is one of the first few values of 0, 1, ... and the enumerator n is one
of the first values of 1, 2, 3, .... See the individual function docstrings for the actual
extents of the lookup tables.
besselj_zero(nu, n)Return the nth zero of the Bessel J function of order nu.
bessely_zero(nu, n)Return the nth zero of the Bessel Y function of order nu.
besselj_deriv_zero(nu, n)Return the nth nonvanishing zero of the derivative of the Bessel J function of order nu.
bessely_deriv_zero(nu, n)Return the nth zero of the derivative of the Bessel Y function of order nu.
FunctionZeros.besselj_zero_asymptotic(nu, n)Asymptotic formula for the nth zero for the Bessel J function of order nu.
FunctionZeros.bessely_zero_asymptotic(nu, n)Asymptotic formula for the nth zero for the Bessel Y function of order nu.
FunctionZeros.besselj_deriv_zero_asymptotic(nu, n)Asymptotic formula for the nth nonvanishing zero of the derivative of the Bessel J function of order nu.
FunctionZeros.bessely_deriv_zero_asymptotic(nu, n)Asymptotic formula for the nth zero of the derivative of the Bessel Y function of order nu.