Overload List
| # | Signature | Description |
|---|---|---|
| 1 | TCplx Besj(double NU, TCplx Z); | Bessel function of the first kind, complex argument: J_(nu)(z). |
| 2 | TSCplx Besj(float NU, TSCplx Z); | |
| 3 | TCplx Besj(double NU, double A); | Bessel function of the first kind, real argument: J_(nu)(x). |
| 4 | TSCplx Besj(float NU, float A); | |
| 5 | TCplx Besj(double NU, TCplx Z, bool Scale); | Bessel function of the first kind, complex argument, optional scaling: J_(nu)(z). |
| 6 | TSCplx Besj(float NU, TSCplx Z, bool Scale); | |
| 7 | void Besj(double NU, TCplx Z, TVec *resCY, bool Scale); | Sequence of Bessel functions of the first kind, complex argument: J_(nu+i)(z), i=0... N-1. |
| 8 | TCplx Besj(double NU, double A, bool Scale); | Bessel function of the first kind, real argument, optional scaling: J_(nu)(x). |
| 9 | TSCplx Besj(float NU, float A, bool Scale); |
Overload 1: TCplx Besj(double NU, TCplx Z);
Bessel function of the first kind, complex argument: J_(nu)(z).
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | double | Defines the order of the Bessel function of the first kind Jn. |
| 2 | Z | TCplx | Defines complex value for which Jn(Z) should be evaluated. |
Returns: J_(nu)(z), the Bessel function of the first kind of order NU, evaluated at the complex argument Z.
J_(nu) is the solution of Bessel's equation z^2 w'' + z w' + (z^2-nu^2)w = 0 that is regular at the origin:
J_(nu)(z) = sum_(m=0)^(inf)((-1)^m)/(m! Gamma(m+nu+1))(z/2)^(2m+nu)
For negative orders the reflection formula J_(-nu)(z)=cos(nupi)J_(nu)(z)-sin(nupi)Y_(nu)(z) is applied. Domain. Any finite complex Z; order NU may be any real value.
Overload 2: TSCplx Besj(float NU, TSCplx Z);
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | float | |
| 2 | Z | TSCplx |
Overload 3: TCplx Besj(double NU, double A);
Bessel function of the first kind, real argument: J_(nu)(x).
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | double | Defines the order of the Bessel function of the first kind Jn. |
| 2 | A | double | Defines real value for which Jn(A) should be evaluated. |
Returns: J_(nu)(x) of order NU at the real argument A. The value is returned as a TCplx; for nu >= 0 and real x >= 0 the imaginary part is zero.
Same definition as the complex overload, J_(nu)(x)=sum_(m >= 0)((-1)^m)/(m! Gamma(m+nu+1))(x/2)^(2m+nu). Domain. Any finite real A; order NU any real value (negative orders use the reflection formula).
Overload 4: TSCplx Besj(float NU, float A);
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | float | |
| 2 | A | float |
Overload 5: TCplx Besj(double NU, TCplx Z, bool Scale);
Bessel function of the first kind, complex argument, optional scaling: J_(nu)(z).
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | double | Defines the order of the Bessel function of the first kind Jn. |
| 2 | Z | TCplx | Defines complex value for which Jn(Z) should be evaluated. |
| 3 | Scale | bool | If Scale parameter is true, Jn(Z) is multiplied by e^(-|Im z|). |
Returns: J_(nu)(z) of order NU. When is true the result is multiplied by e^(-|Im z|), i.e. e^(-|Im z|) J_(nu)(z), which removes the exponential growth along the imaginary axis.
J_(nu)(z) = sum_(m=0)^(inf)((-1)^m)/(m! Gamma(m+nu+1))(z/2)^(2m+nu)
Domain. Any finite complex Z; order NU any real value. Behavior. On argument-reduction
failure for very large |z| the routine raises an exception.
Overload 6: TSCplx Besj(float NU, TSCplx Z, bool Scale);
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | float | |
| 2 | Z | TSCplx | |
| 3 | Scale | bool |
Overload 7: void Besj(double NU, TCplx Z, TVec *resCY, bool Scale);
Sequence of Bessel functions of the first kind, complex argument: J_(nu+i)(z), i=0... N-1.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | double | Defines the order of the Bessel function of the first kind Jn. |
| 2 | Z | TCplx | Defines complex value for which Jn(Z) should be evaluated. |
| 3 | resCY | TVec * | Contains the result, which is an array: resCY[I]=Exp(-Abs(Y))*J(FNU+I,Z) , I = 0...,N-1 , Y=Imag(Z). The part Exp(-Abs(Y)) is applied only if Scaling is True. The length of the array N is specified with resCY.Length on input. |
| 4 | Scale | bool | If Scale parameter is true, Jn(Z) is multiplied by e^(-|Im z|). |
Returns: Fills with J_(nu+i)(z) for i=0,...,N-1, where N is the input length of . When is true each element is multiplied by e^(-|Im z|).
resCY[i] = e^(-|Im z|) J_(nu+i)(z), i=0,...,N-1, the factor e^(-|Im z|) applied only when scaling is enabled. Domain. resCY must be a non-empty complex double vector; z=0 yields -inf.
Overload 8: TCplx Besj(double NU, double A, bool Scale);
Bessel function of the first kind, real argument, optional scaling: J_(nu)(x).
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | double | Defines the order of the Bessel function of the first kind Jn. |
| 2 | A | double | Defines real value for which Jn(A) should be evaluated. |
| 3 | Scale | bool | If Scale parameter is true, Jn(A) is multiplied by e^(-|Im x|). |
Returns: J_(nu)(x) of order NU. When is true the result is multiplied by e^(-|Im x|) (which equals 1 for real x, so scaling has no effect on a real argument).
Domain. Any finite real A; order NU any real value.
Overload 9: TSCplx Besj(float NU, float A, bool Scale);
| # | Name | Type | Description |
|---|---|---|---|
| 1 | NU | float | |
| 2 | A | float | |
| 3 | Scale | bool |