Real zeros of Bessel J functions - 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 v0 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

BesselJZeros0,1

BesselJZeros0,1

(1)

evalfBesselJZeros0,1

2.404825558

(2)

BesselJZeros1.5,10

32.95638904

(3)

BesselJZeros12,5

5π

(4)

BesselYZeros12,5

92π

(5)

BesselJZeros1,0

0

(6)

BesselJZeros1.,3..6

10.17346814,13.32369194,16.47063005,19.61585851

(7)

s:=BesselYZeros1,3..6

s:=BesselYZeros1,3..6

(8)

evalfs

8.596005868,11.74915483,14.89744213,18.04340228

(9)

BesselJv,BesselJZerosv,3

0

(10)

See Also

Bessel, inifcns


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