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Bessel Zeros Calculator

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The Bessel functions BesselJ[ν, x] and BesselY[ν, x] are linearly independent solutions to the differential equation x² y^'' + x y^' + (x² - ν²) y = 0. For integer ν, the J_ν(x) are regular at x = 0, while the Y_ν(x) have a logarithmic divergence at x = 0.

Bessel functions arise in solving differential equations for systems with cylindrical symmetry.

J_ν(x) is often called the Bessel function of the first kind, or simply the Bessel function. Y_ν(x) is referred to as the Bessel function of the second kind, the Weber function, or the Neumann function (denoted N_ν(x)).

Exact solutions to many partial differential equations can be expressed as infinite sums over the zeros of some Bessel function or functions.

Select Bessel function:


Parameters:
             ν          λ

Choose zeros class:
    give a list of the first n zeros
             n
    give a list containing the m^th through the n^th zeros
            m          n
    give a list of the zeros between min and max
         min     max

Options:
         WorkingPrecision
               AccuracyGoal

Result:

To download the generated graphics, click here.
To specify some general 2D graphics options, click here.