Overload List
| # | Signature | Description |
|---|---|---|
| 1 | TCplx Besk(Double NU, TCplx Z) | Modified Bessel function of the second kind, complex argument: K_(nu)(z). |
| 2 | void Besk(Double NU, TCplx Z, TVec resCY, Boolean Scale) | Sequence of modified Bessel functions of the second kind, complex argument: K_(nu+i)(z), i=0... N-1. |
| 3 | TCplx Besk(Double NU, TCplx Z, Boolean Scale) | Modified Bessel function of the second kind, complex argument, optional scaling: K_(nu)(z). |
| 4 | TCplx Besk(Double NU, Double A) | Modified Bessel function of the second kind, real argument: K_(nu)(x). |
| 5 | TCplx Besk(Double NU, Double A, Boolean Scale) | Modified Bessel function of the second kind, real argument, optional scaling: K_(nu)(x). |
| 6 | TSCplx Besk(Single NU, TSCplx Z) | |
| 7 | TSCplx Besk(Single NU, TSCplx Z, Boolean Scale) | |
| 8 | TSCplx Besk(Single NU, Single A) | |
| 9 | TSCplx Besk(Single NU, Single A, Boolean Scale) |
Overload 1: TCplx Besk(Double NU, TCplx Z)
Modified Bessel function of the second kind, complex argument: K_(nu)(z).
| # | Name | Description |
|---|---|---|
| 1 | NU | Defines the order of Hankel function. |
| 2 | Z | Defines complex value for which Kn(Z) should be evaluated. |
Returns: TCplx (complex) - K_(nu)(z), the modified Bessel function of the second kind (Macdonald function) of order NU at Z.
K_(nu) is the decaying solution of the modified Bessel equation; it satisfies K_(-nu)(z)=K_(nu)(z) and K_(nu)(z) = pi/2 (I_(-nu)(z)-I_(nu)(z))/sin(nupi). Domain. Any finite complex Z with z != 0; the principal branch is used. Behavior. At
z=0 the function diverges and the implementation returns +inf in both components.
Overload 2: void Besk(Double NU, TCplx Z, TVec resCY, Boolean Scale)
Sequence of modified Bessel functions of the second kind, complex argument: K_(nu+i)(z), i=0... N-1.
| # | Name | Description |
|---|---|---|
| 1 | NU | Defines the order of Hankel function. |
| 2 | Z | Defines complex value for which Kn((Z) should be evaluated. |
| 3 | resCY | Contains result on output and needs to be sized to desired N on input. The result holds: cyRes[i] = K(NU + i, Z)*Exp(Z) when scaled and cyRes[i] = K(NU + i, Z) when not scaled. |
| 4 | Scale | If Scale parameter is true, Kn(A) is multiplied by e^z. |
Result: stored in self (calling object)
Returns: Fills with K_(nu+i)(z) for i=0,...,N-1 (N = input length of ). When is true each element is multiplied by e^z.
resCY[i] = e^z K_(nu+i)(z), i=0,...,N-1, with the factor applied only when scaling is enabled. Domain. resCY must be a non-empty complex double vector; at z=0 every element is set to +inf.
Overload 3: TCplx Besk(Double NU, TCplx Z, Boolean Scale)
Modified Bessel function of the second kind, complex argument, optional scaling: K_(nu)(z).
| # | Name | Description |
|---|---|---|
| 1 | Z | Defines complex value for which Kn(Z) should be evaluated. |
| 2 | NU | Defines the order of the Bessel function of the second kind Kn. |
| 3 | Scale | If Scale parameter is true, Kn(Z) is multiplied by e^z. |
Returns: TCplx (complex) - K_(nu)(z) of order NU. When is true the result is multiplied by e^z, i.e. e^z K_(nu)(z), which removes the exponential decay for large Re z.
K_(nu)(z) = pi/2 (I_(-nu)(z)-I_(nu)(z))/sin(nupi), K_(-nu)(z)=K_(nu)(z).
Domain. Any finite complex Z with z != 0. Behavior. Returns +inf at z=0.
Overload 4: TCplx Besk(Double NU, Double A)
Modified Bessel function of the second kind, real argument: K_(nu)(x).
| # | Name | Description |
|---|---|---|
| 1 | NU | Defines the order of Hankel function. |
| 2 | A | Defines real value for which Kn(A) should be evaluated. |
Returns: TCplx (complex) - K_(nu)(x) of order NU at the real argument A (returned as a TCplx).
K_(-nu)(x)=K_(nu)(x). Domain. A>0 (real). Behavior. K diverges at x=0, where the implementation returns +inf.
Overload 5: TCplx Besk(Double NU, Double A, Boolean Scale)
Modified Bessel function of the second kind, real argument, optional scaling: K_(nu)(x).
| # | Name | Description |
|---|---|---|
| 1 | A | Defines real value for which Kn(A) should be evaluated. |
| 2 | NU | Defines the order of the Bessel function of the second kind Kn. |
| 3 | Scale | If Scale parameter is true, Kn(A) is multiplied by e^x. |
Returns: TCplx (complex) - K_(nu)(x) of order NU; when is true it is multiplied by e^x.
Domain. A>0 (real). Behavior. Returns +inf at x=0.
Overload 6: TSCplx Besk(Single NU, TSCplx Z)
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | Single | scalar |
| 2 | Z | TSCplx | scalar |
Returns: TSCplx
Overload 7: TSCplx Besk(Single NU, TSCplx Z, Boolean Scale)
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | Single | scalar |
| 2 | Z | TSCplx | scalar |
| 3 | Scale | Boolean |
Returns: TSCplx
Overload 8: TSCplx Besk(Single NU, Single A)
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | Single | scalar |
| 2 | A | Single | scalar |
Returns: TSCplx
Overload 9: TSCplx Besk(Single NU, Single A, Boolean Scale)
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | Single | scalar |
| 2 | A | Single | scalar |
| 3 | Scale | Boolean |
Returns: TSCplx