Class Bessel
- java.lang.Object
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- cern.jet.math.Constants
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- cern.jet.math.Bessel
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public class Bessel extends Constants
Bessel and Airy functions.
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Field Summary
Fields Modifier and Type Field Description protected static double[]
A_i0
Chebyshev coefficients for exp(-x) I0(x) in the interval [0,8].protected static double[]
A_i1
Chebyshev coefficients for exp(-x) I1(x) / x in the interval [0,8].protected static double[]
A_k0
COEFFICIENTS FOR METHODS k0, k0e *protected static double[]
A_k1
COEFFICIENTS FOR METHODS k1, k1e *protected static double[]
B_i0
Chebyshev coefficients for exp(-x) sqrt(x) I0(x) in the inverted interval [8,infinity].protected static double[]
B_i1
protected static double[]
B_k0
protected static double[]
B_k1
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Constructor Summary
Constructors Modifier Constructor Description protected
Bessel()
Makes this class non instantiable, but still let's others inherit from it.
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Method Summary
All Methods Static Methods Concrete Methods Modifier and Type Method Description static double
i0(double x)
Returns the modified Bessel function of order 0 of the argument.static double
i0e(double x)
Returns the exponentially scaled modified Bessel function of order 0 of the argument.static double
i1(double x)
Returns the modified Bessel function of order 1 of the argument.static double
i1e(double x)
Returns the exponentially scaled modified Bessel function of order 1 of the argument.static double
j0(double x)
Returns the Bessel function of the first kind of order 0 of the argument.static double
j1(double x)
Returns the Bessel function of the first kind of order 1 of the argument.static double
jn(int n, double x)
Returns the Bessel function of the first kind of order n of the argument.static double
k0(double x)
Returns the modified Bessel function of the third kind of order 0 of the argument.static double
k0e(double x)
Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.static double
k1(double x)
Returns the modified Bessel function of the third kind of order 1 of the argument.static double
k1e(double x)
Returns the exponentially scaled modified Bessel function of the third kind of order 1 of the argument.static double
kn(int nn, double x)
Returns the modified Bessel function of the third kind of order nn of the argument.static double
y0(double x)
Returns the Bessel function of the second kind of order 0 of the argument.static double
y1(double x)
Returns the Bessel function of the second kind of order 1 of the argument.static double
yn(int n, double x)
Returns the Bessel function of the second kind of order n of the argument.
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Field Detail
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A_i0
protected static final double[] A_i0
Chebyshev coefficients for exp(-x) I0(x) in the interval [0,8]. lim(x->0){ exp(-x) I0(x) } = 1.
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B_i0
protected static final double[] B_i0
Chebyshev coefficients for exp(-x) sqrt(x) I0(x) in the inverted interval [8,infinity]. lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
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A_i1
protected static final double[] A_i1
Chebyshev coefficients for exp(-x) I1(x) / x in the interval [0,8]. lim(x->0){ exp(-x) I1(x) / x } = 1/2.
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B_i1
protected static final double[] B_i1
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A_k0
protected static final double[] A_k0
COEFFICIENTS FOR METHODS k0, k0e *
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B_k0
protected static final double[] B_k0
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A_k1
protected static final double[] A_k1
COEFFICIENTS FOR METHODS k1, k1e *
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B_k1
protected static final double[] B_k1
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Method Detail
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i0
public static double i0(double x) throws java.lang.ArithmeticException
Returns the modified Bessel function of order 0 of the argument.The function is defined as i0(x) = j0( ix ).
The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.
- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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i0e
public static double i0e(double x) throws java.lang.ArithmeticException
Returns the exponentially scaled modified Bessel function of order 0 of the argument.The function is defined as i0e(x) = exp(-|x|) j0( ix ).
- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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i1
public static double i1(double x) throws java.lang.ArithmeticException
Returns the modified Bessel function of order 1 of the argument.The function is defined as i1(x) = -i j1( ix ).
The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.
- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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i1e
public static double i1e(double x) throws java.lang.ArithmeticException
Returns the exponentially scaled modified Bessel function of order 1 of the argument.The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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j0
public static double j0(double x) throws java.lang.ArithmeticException
Returns the Bessel function of the first kind of order 0 of the argument.- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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j1
public static double j1(double x) throws java.lang.ArithmeticException
Returns the Bessel function of the first kind of order 1 of the argument.- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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jn
public static double jn(int n, double x) throws java.lang.ArithmeticException
Returns the Bessel function of the first kind of order n of the argument.- Parameters:
n
- the order of the Bessel function.x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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k0
public static double k0(double x) throws java.lang.ArithmeticException
Returns the modified Bessel function of the third kind of order 0 of the argument.The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.
- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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k0e
public static double k0e(double x) throws java.lang.ArithmeticException
Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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k1
public static double k1(double x) throws java.lang.ArithmeticException
Returns the modified Bessel function of the third kind of order 1 of the argument.The range is partitioned into the two intervals [0,2] and (2, infinity). Chebyshev polynomial expansions are employed in each interval.
- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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k1e
public static double k1e(double x) throws java.lang.ArithmeticException
Returns the exponentially scaled modified Bessel function of the third kind of order 1 of the argument.k1e(x) = exp(x) * k1(x).
- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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kn
public static double kn(int nn, double x) throws java.lang.ArithmeticException
Returns the modified Bessel function of the third kind of order nn of the argument.The range is partitioned into the two intervals [0,9.55] and (9.55, infinity). An ascending power series is used in the low range, and an asymptotic expansion in the high range.
- Parameters:
nn
- the order of the Bessel function.x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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y0
public static double y0(double x) throws java.lang.ArithmeticException
Returns the Bessel function of the second kind of order 0 of the argument.- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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y1
public static double y1(double x) throws java.lang.ArithmeticException
Returns the Bessel function of the second kind of order 1 of the argument.- Parameters:
x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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yn
public static double yn(int n, double x) throws java.lang.ArithmeticException
Returns the Bessel function of the second kind of order n of the argument.- Parameters:
n
- the order of the Bessel function.x
- the value to compute the bessel function of.- Throws:
java.lang.ArithmeticException
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