BesselJZeros - Maple Help

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BesselJZeros

Real zeros of Bessel J functions

BesselYZeros

Real zeros of Bessel Y functions

 Calling Sequence BesselJZeros(v, n) BesselJZeros(v, n1..n2) BesselYZeros(v, n) BesselYZeros(v, n1..n2)

Parameters

 v - algebraic expression (the order of the Bessel function) n - algebraic expression (the index of a zero) n1, n2 - algebraic expressions (a range n1..n2 of indices for consecutive zeros)

Description

 • BesselJZeros(v, n) denotes the n-th positive real root of the BesselJ function of order v.
 - If v is numeric, then it must be a real constant. If v is a float, then a numerical evaluation is attempted, otherwise a symbolic representation is returned.
 - If n is numeric, then it must be a positive integer.
 • BesselJZeros(v, n1..n2) represents the sequence of consecutive zeros with index from n1 to n2.
 • BesselYZeros(v, n) and BesselYZeros(v, n1..n2) correspond to the zeros of the BesselY function.
 • Note that if $v\ne 0$ then BesselJZeros(v, 0) is also defined and is equal to 0.
 • These functions may use fsolve to find a floating point approximation for the zeros. To solve ill-conditioned problems, it is convenient to assign the name 'fulldigits' to the environment variable_Envfulldigits.

Examples

 > $\mathrm{BesselJZeros}\left(0,1\right)$
 ${\mathrm{BesselJZeros}}{}\left({0}{,}{1}\right)$ (1)
 > $\mathrm{evalf}\left(\mathrm{BesselJZeros}\left(0,1\right)\right)$
 ${2.404825558}$ (2)
 > $\mathrm{BesselJZeros}\left(1.5,10\right)$
 ${32.95638904}$ (3)
 > $\mathrm{BesselJZeros}\left(\frac{1}{2},5\right)$
 ${5}{}{\mathrm{π}}$ (4)
 > $\mathrm{BesselYZeros}\left(\frac{1}{2},5\right)$
 $\frac{{9}}{{2}}{}{\mathrm{π}}$ (5)
 > $\mathrm{BesselJZeros}\left(1,0\right)$
 ${0}$ (6)
 > $\mathrm{BesselJZeros}\left(1.,3..6\right)$
 ${10.17346814}{,}{13.32369194}{,}{16.47063005}{,}{19.61585851}$ (7)
 > $s≔\mathrm{BesselYZeros}\left(1,3..6\right)$
 ${s}{:=}{\mathrm{BesselYZeros}}{}\left({1}{,}{3}{..}{6}\right)$ (8)
 > $\mathrm{evalf}\left(s\right)$
 ${8.596005868}{,}{11.74915483}{,}{14.89744213}{,}{18.04340228}$ (9)
 > $\mathrm{BesselJ}\left(v,\mathrm{BesselJZeros}\left(v,3\right)\right)$
 ${0}$ (10)