BesselRelated (FsODE)

FsODE

Documentation for 0.0.2

BesselRelated Type

Namespace: Altaxo.Calc
Assembly: AltaxoCore.Redist.dll
Base Type: obj

Bessel functions for integer order.

Constructors

Constructor	Description
`BesselRelated()` Full Usage: `BesselRelated()`

Static members

Static member	Description
`BesselRelated.AiryAi(x)` Full Usage: `BesselRelated.AiryAi(x)` Parameters: x : `float` - The function argument. Returns: `float` Airy function for argument x.	AiryAi(x) calculates the double precision Airy function for double precision argument x. x : `float` The function argument. Returns: `float` Airy function for argument x.
`BesselRelated.AiryAi(x, bDebug)` Full Usage: `BesselRelated.AiryAi(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Airy function for argument x.	AiryAi(x) calculates the double precision Airy function for double precision argument x. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Airy function for argument x.
`BesselRelated.AiryBi(x)` Full Usage: `BesselRelated.AiryBi(x)` Parameters: x : `float` - The function argument. Returns: `float` Airy function of the second kind for double precision argument x.	AiryBi(x) calculates the double precision Airy function of the second kind for double precision argument x. x : `float` The function argument. Returns: `float` Airy function of the second kind for double precision argument x.
`BesselRelated.AiryBi(x, bDebug)` Full Usage: `BesselRelated.AiryBi(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Airy function of the second kind for double precision argument x.	AiryBi(x) calculates the double precision Airy function of the second kind for double precision argument x. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Airy function of the second kind for double precision argument x.
`BesselRelated.AiryExpAi(x)` Full Usage: `BesselRelated.AiryExpAi(x)` Parameters: x : `float` - The function argument. Returns: `float` Airy function or the exponentially scaled Airy function depending on the value of the argument.	AiryExpAi(x) calculates the Airy function or the exponentially scaled Airy function depending on the value of the argument. The function and argument are both double precision. Returns Ai(x) for x <= 0.0 Ai(x) * exp(2/3 * x^(3/2)) for x >= 0.0. x : `float` The function argument. Returns: `float` Airy function or the exponentially scaled Airy function depending on the value of the argument.
`BesselRelated.AiryExpAi(x, bDebug)` Full Usage: `BesselRelated.AiryExpAi(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Airy function or the exponentially scaled Airy function depending on the value of the argument.	AiryExpAi(x) calculates the Airy function or the exponentially scaled Airy function depending on the value of the argument. The function and argument are both double precision. Returns Ai(x) for x <= 0.0 Ai(x) * exp(2/3 * x^(3/2)) for x >= 0.0. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Airy function or the exponentially scaled Airy function depending on the value of the argument.
`BesselRelated.AiryExpBi(x)` Full Usage: `BesselRelated.AiryExpBi(x)` Parameters: x : `float` - The function argument. Returns: `float` Airy function of the second kind or the exponentially scaled Airy function of the second kind, depending on the value of the argument x.	AiryExpBi(x) calculates the double precision Airy function of the second kind or the double precision exponentially scaled Airy function of the second kind, depending on the value of the double precision argument x. Returns Bi(x) for x <= 0.0 Bi(x)exp( -2/3 x^(3/2)) for x >= 0.0 x : `float` The function argument. Returns: `float` Airy function of the second kind or the exponentially scaled Airy function of the second kind, depending on the value of the argument x.
`BesselRelated.AiryExpBi(x, bDebug)` Full Usage: `BesselRelated.AiryExpBi(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Airy function of the second kind or the exponentially scaled Airy function of the second kind, depending on the value of the argument x.	AiryExpBi(x) calculates the double precision Airy function of the second kind or the double precision exponentially scaled Airy function of the second kind, depending on the value of the double precision argument x. Returns Bi(x) for x <= 0.0 Bi(x)exp( -2/3 x^(3/2)) for x >= 0.0 x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Airy function of the second kind or the exponentially scaled Airy function of the second kind, depending on the value of the argument x.
`BesselRelated.BesselExpI0(x)` Full Usage: `BesselRelated.BesselExpI0(x)` Parameters: x : `float` - The function argument. Returns: `float` The exponentially scaled modified (hyperbolic) Bessel function of the first kind of order zero for argument x.	BesselExpI0(x) calculates the double precision exponentially scaled modified (hyperbolic) Bessel function of the first kind of order zero for double precision argument x. The result is the Bessel function i0(X) multiplied by exp(-abs(x)). x : `float` The function argument. Returns: `float` The exponentially scaled modified (hyperbolic) Bessel function of the first kind of order zero for argument x.
`BesselRelated.BesselExpI0(x, bDebug)` Full Usage: `BesselRelated.BesselExpI0(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` The exponentially scaled modified (hyperbolic) Bessel function of the first kind of order zero for argument x.	BesselExpI0(x) calculates the double precision exponentially scaled modified (hyperbolic) Bessel function of the first kind of order zero for double precision argument x. The result is the Bessel function i0(X) multiplied by exp(-abs(x)). x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` The exponentially scaled modified (hyperbolic) Bessel function of the first kind of order zero for argument x.
`BesselRelated.BesselExpI1(x)` Full Usage: `BesselRelated.BesselExpI1(x)` Parameters: x : `float` - The function argument. Returns: `float` The exponentially scaled modified (hyperbolic) Bessel function of the first kind of order one for argument x.	BesselExpI1(x) calculates the double precision exponentially scaled modified (hyperbolic) Bessel function of the first kind of order one for double precision argument x. The result is I1(x) multiplied by exp(-abs(x)). x : `float` The function argument. Returns: `float` The exponentially scaled modified (hyperbolic) Bessel function of the first kind of order one for argument x.
`BesselRelated.BesselExpI1(x, bDebug)` Full Usage: `BesselRelated.BesselExpI1(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` The exponentially scaled modified (hyperbolic) Bessel function of the first kind of order one for argument x.	BesselExpI1(x) calculates the double precision exponentially scaled modified (hyperbolic) Bessel function of the first kind of order one for double precision argument x. The result is I1(x) multiplied by exp(-abs(x)). x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` The exponentially scaled modified (hyperbolic) Bessel function of the first kind of order one for argument x.
`BesselRelated.BesselExpK0(x)` Full Usage: `BesselRelated.BesselExpK0(x)` Parameters: x : `float` - The function argument. Returns: `float` Exponentially scaled modified (hyperbolic) Bessel function of the third kind of order zero for positive double precision argument x.	BesselExpK0 (x) computes the double precision exponentially scaled modified (hyperbolic) Bessel function of the third kind of order zero for positive double precision argument X. x : `float` The function argument. Returns: `float` Exponentially scaled modified (hyperbolic) Bessel function of the third kind of order zero for positive double precision argument x.
`BesselRelated.BesselExpK0(x, bDebug)` Full Usage: `BesselRelated.BesselExpK0(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Exponentially scaled modified (hyperbolic) Bessel function of the third kind of order zero for positive double precision argument x.	BesselExpK0 (x) computes the double precision exponentially scaled modified (hyperbolic) Bessel function of the third kind of order zero for positive double precision argument X. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Exponentially scaled modified (hyperbolic) Bessel function of the third kind of order zero for positive double precision argument x.
`BesselRelated.BesselExpK1(x)` Full Usage: `BesselRelated.BesselExpK1(x)` Parameters: x : `float` - The function argument. Returns: `float` Exponentially scaled modified (hyperbolic) Bessel function of the third kind of order one for positive double precision argument x.	BesselExpK1(x) computes the double precision exponentially scaled modified (hyperbolic) Bessel function of the third kind of order one for positive double precision argument x. x : `float` The function argument. Returns: `float` Exponentially scaled modified (hyperbolic) Bessel function of the third kind of order one for positive double precision argument x.
`BesselRelated.BesselExpK1(x, bDebug)` Full Usage: `BesselRelated.BesselExpK1(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Exponentially scaled modified (hyperbolic) Bessel function of the third kind of order one for positive double precision argument x.	BesselExpK1(x) computes the double precision exponentially scaled modified (hyperbolic) Bessel function of the third kind of order one for positive double precision argument x. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Exponentially scaled modified (hyperbolic) Bessel function of the third kind of order one for positive double precision argument x.
`BesselRelated.BesselI0(x)` Full Usage: `BesselRelated.BesselI0(x)` Parameters: x : `float` - The function argument. Returns: `float` Modified (hyperbolic) Bessel function of the first kind of order zero and double precision argument x.	BesselI0(x) calculates the double precision modified (hyperbolic) Bessel function of the first kind of order zero and double precision argument x. x : `float` The function argument. Returns: `float` Modified (hyperbolic) Bessel function of the first kind of order zero and double precision argument x.
`BesselRelated.BesselI0(x, bDebug)` Full Usage: `BesselRelated.BesselI0(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Modified (hyperbolic) Bessel function of the first kind of order zero and double precision argument x.	BesselI0(x) calculates the double precision modified (hyperbolic) Bessel function of the first kind of order zero and double precision argument x. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Modified (hyperbolic) Bessel function of the first kind of order zero and double precision argument x.
`BesselRelated.BesselI1(x)` Full Usage: `BesselRelated.BesselI1(x)` Parameters: x : `float` - The function argument. Returns: `float` The modified (hyperbolic) Bessel function of the first kind of order one and double precision argument x.	BesselI1(x) calculates the double precision modified (hyperbolic) Bessel function of the first kind of order one and double precision argument x. x : `float` The function argument. Returns: `float` The modified (hyperbolic) Bessel function of the first kind of order one and double precision argument x.
`BesselRelated.BesselI1(x, bDebug)` Full Usage: `BesselRelated.BesselI1(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` The modified (hyperbolic) Bessel function of the first kind of order one and double precision argument x.	BesselI1(x) calculates the double precision modified (hyperbolic) Bessel function of the first kind of order one and double precision argument x. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` The modified (hyperbolic) Bessel function of the first kind of order one and double precision argument x.
`BesselRelated.BesselJ(n, x)` Full Usage: `BesselRelated.BesselJ(n, x)` Parameters: n : `int` - The order of the bessel function. x : `float` - The function argument. Returns: `float` Bessel function of the first kind of order n for argument x.	BesselJ(n,x) calculates the double precision Bessel function of the first kind of order n for double precision argument x. Miller's downward recurrence algorithm is used. Implemented by B. M. Gammel, last revision 13.03.1996 n : `int` The order of the bessel function. x : `float` The function argument. Returns: `float` Bessel function of the first kind of order n for argument x.
`BesselRelated.BesselJ(n, x, bDebug)` Full Usage: `BesselRelated.BesselJ(n, x, bDebug)` Parameters: n : `int` - The order of the bessel function. x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the first kind of order n for argument x.	BesselJ(n,x) calculates the double precision Bessel function of the first kind of order n for double precision argument x. Miller's downward recurrence algorithm is used. Implemented by B. M. Gammel, last revision 13.03.1996 n : `int` The order of the bessel function. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the first kind of order n for argument x.
`BesselRelated.BesselJ0(x)` Full Usage: `BesselRelated.BesselJ0(x)` Parameters: x : `float` - The function argument. Returns: `float` Bessel function of the first kind of order zero for argument x.	BesselJ0(x) calculates the double precision Bessel function of the first kind of order zero for double precision argument x. x : `float` The function argument. Returns: `float` Bessel function of the first kind of order zero for argument x.
`BesselRelated.BesselJ0(x, bDebug)` Full Usage: `BesselRelated.BesselJ0(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the first kind of order zero for argument x.	BesselJ0(x) calculates the double precision Bessel function of the first kind of order zero for double precision argument x. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the first kind of order zero for argument x.
`BesselRelated.BesselJ1(x)` Full Usage: `BesselRelated.BesselJ1(x)` Parameters: x : `float` - The function argument. Returns: `float` Bessel function of the first kind of order one for argument x.	BesselJ1(x) calculates the double precision Bessel function of the first kind of order one for double precision argument x. x : `float` The function argument. Returns: `float` Bessel function of the first kind of order one for argument x.
`BesselRelated.BesselJ1(x, bDebug)` Full Usage: `BesselRelated.BesselJ1(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the first kind of order one for argument x.	BesselJ1(x) calculates the double precision Bessel function of the first kind of order one for double precision argument x. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the first kind of order one for argument x.
`BesselRelated.BesselK0(x)` Full Usage: `BesselRelated.BesselK0(x)` Parameters: x : `float` - The function argument. Returns: `float` Modified (hyperbolic) Bessel function of the third kind of order zero for double precision argument x.	BesselK0(x) calculates the double precision modified (hyperbolic) Bessel function of the third kind of order zero for double precision argument x. The argument must be greater than zero but not so large that the result underflows. x : `float` The function argument. Returns: `float` Modified (hyperbolic) Bessel function of the third kind of order zero for double precision argument x.
`BesselRelated.BesselK0(x, bDebug)` Full Usage: `BesselRelated.BesselK0(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Modified (hyperbolic) Bessel function of the third kind of order zero for double precision argument x.	BesselK0(x) calculates the double precision modified (hyperbolic) Bessel function of the third kind of order zero for double precision argument x. The argument must be greater than zero but not so large that the result underflows. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Modified (hyperbolic) Bessel function of the third kind of order zero for double precision argument x.
`BesselRelated.BesselK1(x)` Full Usage: `BesselRelated.BesselK1(x)` Parameters: x : `float` - The function argument. Returns: `float` Modified (hyperbolic) Bessel function of the third kind of order one for double precision argument x.	BesselK1(x) calculates the double precision modified (hyperbolic) Bessel function of the third kind of order one for double precision argument x. The argument must be large enough that the result does not overflow and small enough that the result does not underflow. x : `float` The function argument. Returns: `float` Modified (hyperbolic) Bessel function of the third kind of order one for double precision argument x.
`BesselRelated.BesselK1(x, bDebug)` Full Usage: `BesselRelated.BesselK1(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Modified (hyperbolic) Bessel function of the third kind of order one for double precision argument x.	BesselK1(x) calculates the double precision modified (hyperbolic) Bessel function of the third kind of order one for double precision argument x. The argument must be large enough that the result does not overflow and small enough that the result does not underflow. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Modified (hyperbolic) Bessel function of the third kind of order one for double precision argument x.
`BesselRelated.BesselY(n, x)` Full Usage: `BesselRelated.BesselY(n, x)` Parameters: n : `int` - The order of the Bessel function. x : `float` - The function argument. Returns: `float` Bessel function of the second kind of order n for argument x.	BesselY(n,x) calculates the double precision Bessel function of the second kind of order n for double precision argument x. Implemented by B. M. Gammel, last revision 13.03.1996 n : `int` The order of the Bessel function. x : `float` The function argument. Returns: `float` Bessel function of the second kind of order n for argument x.
`BesselRelated.BesselY(n, x, bDebug)` Full Usage: `BesselRelated.BesselY(n, x, bDebug)` Parameters: n : `int` - The order of the Bessel function. x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the second kind of order n for argument x.	BesselY(n,x) calculates the double precision Bessel function of the second kind of order n for double precision argument x. Implemented by B. M. Gammel, last revision 13.03.1996 n : `int` The order of the Bessel function. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the second kind of order n for argument x.
`BesselRelated.BesselY0(x)` Full Usage: `BesselRelated.BesselY0(x)` Parameters: x : `float` - The function argument. Returns: `float` Bessel function of the second kind of order zero for argument x.	BesselY0(x) calculates the double precision Bessel function of the second kind of order zero for double precision argument X. x : `float` The function argument. Returns: `float` Bessel function of the second kind of order zero for argument x.
`BesselRelated.BesselY0(x, bDebug)` Full Usage: `BesselRelated.BesselY0(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the second kind of order zero for argument x.	BesselY0(x) calculates the double precision Bessel function of the second kind of order zero for double precision argument X. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the second kind of order zero for argument x.
`BesselRelated.BesselY1(x)` Full Usage: `BesselRelated.BesselY1(x)` Parameters: x : `float` - The function argument. Returns: `float` Bessel function of the second kind of order for argument x.	BesselY1(x) calculates the double precision Bessel function of the second kind of order for double precision argument x. x : `float` The function argument. Returns: `float` Bessel function of the second kind of order for argument x.
`BesselRelated.BesselY1(x, bDebug)` Full Usage: `BesselRelated.BesselY1(x, bDebug)` Parameters: x : `float` - The function argument. bDebug : `bool` - If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the second kind of order for argument x.	BesselY1(x) calculates the double precision Bessel function of the second kind of order for double precision argument x. x : `float` The function argument. bDebug : `bool` If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors. Returns: `float` Bessel function of the second kind of order for argument x.