Overload List
| # | Signature | Description |
|---|---|---|
| 1 | function Besi(NU: Double; Z: TCplx): TCplx; | Modified Bessel function of the first kind, complex argument: I_(nu)(z). |
| 2 | procedure Besi(NU: Double; const Z: TCplx; const resCY: TVec; Scale: Boolean); | Sequence of modified Bessel functions of the first kind, complex argument: I_(nu+i)(z), i=0... N-1. |
| 3 | function Besi(NU: Double; Z: TCplx; Scale: Boolean): TCplx; | Modified Bessel function of the first kind, complex argument, optional scaling: I_(nu)(z). |
| 4 | function Besi(NU: Double; A: Double): TCplx; | Modified Bessel function of the first kind, real argument: I_(nu)(x). |
| 5 | function Besi(NU: Double; A: Double; Scale: Boolean): TCplx; | Modified Bessel function of the first kind, real argument, optional scaling: I_(nu)(x). |
| 6 | function Besi(NU: Single; Z: TSCplx): TSCplx; | |
| 7 | function Besi(NU: Single; Z: TSCplx; Scale: Boolean): TSCplx; | |
| 8 | function Besi(NU: Single; A: Single): TSCplx; | |
| 9 | function Besi(NU: Single; A: Single; Scale: Boolean): TSCplx; |
Overload 1: function Besi(NU: Double; Z: TCplx): TCplx;
Modified Bessel function of the first kind, complex argument: I_(nu)(z).
| # | Name | Description |
|---|---|---|
| 1 | NU | Defines the order of In(Z). |
| 2 | Z | Defines complex value for which In(Z) should be evaluated. |
Returns: TCplx (complex) - I_(nu)(z), the modified Bessel function of the first kind of order NU at the complex argument Z.
I_(nu) solves the modified Bessel equation z^2 w'' + z w' - (z^2+nu^2)w = 0 and is regular at the origin: I_(nu)(z) = sum_(m=0)^(inf)1/(m! Gamma(m+nu+1))(z/2)^(2m+nu)
Domain. Any finite complex Z; order NU any real value.
Overload 2: procedure Besi(NU: Double; const Z: TCplx; const resCY: TVec; Scale: Boolean);
Sequence of modified Bessel functions of the first kind, complex argument: I_(nu+i)(z), i=0... N-1.
| # | Name | Description |
|---|---|---|
| 1 | Z | Defines complex value for which In(Z) should be evaluated. |
| 2 | NU | Defines the order of the Bessel function of the first kind In. |
| 3 | Scale | If Scale parameter is true, In(Z) is multiplied by e^(-|Re z|). |
| 4 | resCY | Contains result on output and needs to be sized to desired N on input. The result holds: cyRes[j] = I(NU + j, Z)*Exp(-|Re(A)|) when scaled and cyRes[j] = I(NU + j, Z) otherwise. |
Result: stored in self (calling object)
Returns: Fills with I_(nu+i)(z) for i=0,...,N-1 (N = input length of ). When is true each element is multiplied by e^(-|Re z|).
resCY[i] = e^(-|Re z|) I_(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.
Overload 3: function Besi(NU: Double; Z: TCplx; Scale: Boolean): TCplx;
Modified Bessel function of the first kind, complex argument, optional scaling: I_(nu)(z).
| # | Name | Description |
|---|---|---|
| 1 | Z | Defines complex value for which In(Z) should be evaluated. |
| 2 | NU | Defines the order of the Bessel function of the first kind In. |
| 3 | Scale | If Scale parameter is true, In(Z) is multiplied by e^(-|Re z|). |
Returns: TCplx (complex) - I_(nu)(z) of order NU. When is true the result is multiplied by e^(-|Re z|), i.e. e^(-|Re z|) I_(nu)(z), which removes the exponential growth for large Re z.
I_(nu)(z) = sum_(m=0)^(inf)1/(m! Gamma(m+nu+1))(z/2)^(2m+nu)
Domain. Any finite complex Z; order NU any real value.
Overload 4: function Besi(NU: Double; A: Double): TCplx;
Modified Bessel function of the first kind, real argument: I_(nu)(x).
| # | Name | Description |
|---|---|---|
| 1 | NU | Defines the order of In(A). |
| 2 | A | Defines real value for which In(A) should be evaluated. |
Returns: TCplx (complex) - I_(nu)(x) of order NU at the real argument A, returned as a TCplx (imaginary part zero for x >= 0).
I_(nu)(x) = sum_(m=0)^(inf)1/(m! Gamma(m+nu+1))(x/2)^(2m+nu) Domain. Any finite real A; order NU any real value.
Overload 5: function Besi(NU: Double; A: Double; Scale: Boolean): TCplx;
Modified Bessel function of the first kind, real argument, optional scaling: I_(nu)(x).
| # | Name | Description |
|---|---|---|
| 1 | A | Defines real value for which In(A) should be evaluated. |
| 2 | NU | Defines the order of the Bessel function of the first kind In. |
| 3 | Scale | If Scale parameter is true, In(A) is multiplied by e^(-|Re x|). |
Returns: TCplx (complex) - I_(nu)(x) of order NU; when is true it is multiplied by e^(-|x|).
Domain. Any finite real A; order NU any real value.
Overload 6: function Besi(NU: Single; Z: TSCplx): TSCplx;
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | Single | scalar |
| 2 | Z | TSCplx | scalar |
Returns: TSCplx
Overload 7: function Besi(NU: Single; Z: TSCplx; Scale: Boolean): TSCplx;
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | Single | scalar |
| 2 | Z | TSCplx | scalar |
| 3 | Scale | Boolean |
Returns: TSCplx
Overload 8: function Besi(NU: Single; A: Single): TSCplx;
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | Single | scalar |
| 2 | A | Single | scalar |
Returns: TSCplx
Overload 9: function Besi(NU: Single; A: Single; Scale: Boolean): TSCplx;
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | Single | scalar |
| 2 | A | Single | scalar |
| 3 | Scale | Boolean |
Returns: TSCplx