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BesselJZero

BesselJZero[n, k]
represents the k^(th) zero of the Bessel function J_n(x).
BesselJZero[n, k, x0]
represents the k^(th) zero greater than x0.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • N[BesselJZero[n, k]] gives a numerical approximation so long as the specified zero exists.
  • BesselJZero[n, k] represents the k^(th) zero greater than 0.
  • BesselJZero can be evaluated to arbitrary numerical precision.
EXAMPLESCLOSE ALL
Basic Examples   (2)
Evaluate numerically:
Evaluate symbolically:
Evaluate numerically:
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Click for copyable input
Out[1]=
 
Evaluate symbolically:
In[1]:=
Click for copyable input
Out[1]=
Scope   (4)
Evaluate to high precision:
Find the first zero of J_0(x) greater than 100:
BesselJZero threads element-wise over lists:
TraditionalForm formatting:
Generalizations & Extensions   (2)
Find a zero of J_nu(x) cos(alpha)-Y_nu(x) sin(alpha) using BesselJZero[Nu, k-Alpha/Pi]:
Find the derivative of Bessel zero with respect to k:
Applications   (2)
Find the first ten eigenmodes of a circular drum with Dirichlet boundary conditions:
Construct an amplitude comprising a certain mixture of modes:
Circular density plot:
Radial drum displacement profile:
Find the coefficient in the Rayleigh criterion for diffraction-limited optics:
Properties & Relations   (1)
Asymptotic behavior of BesselJZero[Nu, k] for large k:
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