Overload List
| # | Signature | Description |
|---|---|---|
| 1 | function Biry(Z: TCplx): TCplx; | Airy function of the second kind, complex argument: $Bi(z)$. |
| 2 | function Biry(Z: TCplx; Derive: Boolean; Scale: Boolean; var Error: Integer): TCplx; | Airy function of the second kind or its derivative, complex argument, optional scaling: $Bi(z)orBi'(z)$. |
| 3 | function Biry(Z: TSCplx): TSCplx; | |
| 4 | function Biry(Z: TSCplx; Derive: Boolean; Scale: Boolean; var Error: Integer): TSCplx; | |
| 5 | function Biry(A: Double): Double; | Airy function of the second kind, real argument: $Bi(x)$. |
| 6 | function Biry(A: Double; Derive: Boolean; Scale: Boolean; var Error: Integer): Double; | Airy function of the second kind or its derivative, real argument, optional scaling: $Bi(x)orBi'(x)$. |
| 7 | function Biry(A: Single): Single; | |
| 8 | function Biry(A: Single; Derive: Boolean; Scale: Boolean; var Error: Integer): Single; |
Overload 1: function Biry(Z: TCplx): TCplx;
Airy function of the second kind, complex argument: .
| # | Name | Description |
|---|---|---|
| 1 | Z | Defines complex value where BI should be evaluated. |
Returns: TCplx (complex) - $Bi(z)$, the Airy function of the second kind, evaluated for the complex argument Z.
Bi is the dominant solution of w'' = z w, related to the modified Bessel functions by Bi(z) = sqrt(z/3)[I_(-1/3)(2/3z^(3/2))+I_(1/3)(2/3z^(3/2))].
Domain. Any finite complex Z; principal branch of z^(3/2).
Overload 2: function Biry(Z: TCplx; Derive: Boolean; Scale: Boolean; var Error: Integer): TCplx;
Airy function of the second kind or its derivative, complex argument, optional scaling: .
| # | Name | Description |
|---|---|---|
| 1 | Z | Function independant variable, complex value. |
| 2 | Error | Returns error code after the calculation. Return values are: * 0, Normal return - Computation completed. * 1, input error - no computation. * 2, overflow - no computation |
| 3 | dreal(zta)- too large with Scaling=false. * 3, zabs(z) large - computation completed. Losses of signifcance by argument reduction produce less than half of machine accuracy. * 4, zabs(z) too large - no computation | |
| 4 | complete loss of accuracy by argument reduction. * 5, error - no computation | |
| 5 | algorithm termination condition not met. | |
| 6 | Derive | If true, function will return Airy (BI) derivative instead of the actual Airy (BI) function. |
| 7 | Scale | If true, result function (BI) or it's derivative is scaled by e^(-|Rezeta|), where zeta=2/3 z^(3/2). |
Returns: TCplx (complex) - If is false, returns the Airy function of the second kind (BI).
If Derive is true, the derivative of the Airy function of the second kind (BI) is returned. When Scale is true the result is additionally multiplied by e^(-|Rezeta|), zeta=2/3 z^(3/2):
e^(-|Rezeta|) Bi(z) or e^(-|Rezeta|) Bi'(z).
Domain. Any finite complex Z; principal branch of z^(3/2). Behavior. Error is
0 on normal return and otherwise carries the AMOS diagnostic code.
Overload 3: function Biry(Z: TSCplx): TSCplx;
| # | Name | Type | Description |
|---|---|---|---|
| 1 | Z | TSCplx | scalar |
Returns: TSCplx
Overload 4: function Biry(Z: TSCplx; Derive: Boolean; Scale: Boolean; var Error: Integer): TSCplx;
| # | Name | Type | Description |
|---|---|---|---|
| 1 | Z | TSCplx | scalar |
| 2 | Derive | Boolean | |
| 3 | Scale | Boolean | |
| 4 | Error | Integer |
Returns: TSCplx
Overload 5: function Biry(A: Double): Double;
Airy function of the second kind, real argument: .
| # | Name | Description |
|---|---|---|
| 1 | A | Defines real value where BI should be evaluated. |
Returns: Double - $Bi(x)$, the Airy function of the second kind, evaluated for the real argument A. The result is real.
Bi is the second, dominant solution of the Airy equation w'' = z w:
Bi(x) = 1/piintegral _0^(inf)[exp(-t^3/3+x t)+sin(t^3/3+x t)]dt
Domain. Any finite real A. Behavior. Unscaled, non-derivative; grows like
e^((2/3)x^(3/2)) for large positive x, so the underlying routine may raise on overflow.
Overload 6: function Biry(A: Double; Derive: Boolean; Scale: Boolean; var Error: Integer): Double;
Airy function of the second kind or its derivative, real argument, optional scaling: .
| # | Name | Description |
|---|---|---|
| 1 | A | Defines real value where BI or its derivative should be evaluated. |
| 2 | Derive | If true, function will return Airy (BI) derivative instead of the actual Airy (BI) function. |
| 3 | Scale | If true, result function (BI) or it's derivative is scaled by e^(-|Rezeta|), where zeta=2/3 z^(3/2). |
| 4 | Error | Returns error code after the calculation. Return values are: * 0, Normal return - Computation completed. * 1, input error - no computation. * 2, overflow - no computation |
| 5 | dreal(zta)- too large with Scaling=false. * 3, zabs(z) large - computation completed. Losses of signifcance by argument reduction produce less than half of machine accuracy. * 4, zabs(z) too large - no computation | |
| 6 | complete loss of accuracy by argument reduction. * 5, error - no computation | |
| 7 | algorithm termination condition not met. |
Returns: Double - $Bi(x)$, or its derivative $Bi'(x)$ when is true. The result is real.
When Scale is true the result is multiplied by e^(-|Rezeta|) with zeta=2/3 x^(3/2):
e^(-|Rezeta|) Bi(x) or e^(-|Rezeta|) Bi'(x), zeta=2/3 x^(3/2).
Domain. Any finite real A. Behavior. Error is 0 on normal return and
carries the AMOS diagnostic code otherwise (reported, not raised, for this overload).
Overload 7: function Biry(A: Single): Single;
| # | Name | Type | Description |
|---|---|---|---|
| 1 | A | Single | scalar |
Returns: Single
Overload 8: function Biry(A: Single; Derive: Boolean; Scale: Boolean; var Error: Integer): Single;
| # | Name | Type | Description |
|---|---|---|---|
| 1 | A | Single | scalar |
| 2 | Derive | Boolean | |
| 3 | Scale | Boolean | |
| 4 | Error | Integer |
Returns: Single