bessel_j

Overloads

Name	Description
bessel_j(integer nu, integer x) -> real	Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:...
bessel_j(integer nu, real x) -> real	Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:...
bessel_j(integer nu, bool x) -> real	Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:...
bessel_j(real nu, integer x) -> real	Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:...
bessel_j(real nu, real x) -> real	Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:...
bessel_j(real nu, bool x) -> real	Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:...
bessel_j(bool nu, integer x) -> real	Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:...
bessel_j(bool nu, bool x) -> real	Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:...
bessel_j(bool nu, real x) -> real	Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:...

bessel_j(integer nu, integer x) -> real

Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:

$$J_{\nu}(x) = \sum_{m=0}^{\infty} \frac{(-1)^m}{m!\,\[Gamma](../../random/Types/gamma/index.md)(m+\nu+1)} \left(\frac{x}{2}\right)^{2m+\nu}$$

Parameters

• nu: The order of the function.
• x: The value at which the function is evaluated.

bessel_j(integer nu, real x) -> real

Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:

$$J_{\nu}(x) = \sum_{m=0}^{\infty} \frac{(-1)^m}{m!\,\[Gamma](../../random/Types/gamma/index.md)(m+\nu+1)} \left(\frac{x}{2}\right)^{2m+\nu}$$

Parameters

• nu: The order of the function.
• x: The value at which the function is evaluated.

bessel_j(integer nu, bool x) -> real

Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:

$$J_{\nu}(x) = \sum_{m=0}^{\infty} \frac{(-1)^m}{m!\,\[Gamma](../../random/Types/gamma/index.md)(m+\nu+1)} \left(\frac{x}{2}\right)^{2m+\nu}$$

Parameters

• nu: The order of the function.
• x: The value at which the function is evaluated.

bessel_j(real nu, integer x) -> real

Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:

$$J_{\nu}(x) = \sum_{m=0}^{\infty} \frac{(-1)^m}{m!\,\[Gamma](../../random/Types/gamma/index.md)(m+\nu+1)} \left(\frac{x}{2}\right)^{2m+\nu}$$

Parameters

• nu: The order of the function.
• x: The value at which the function is evaluated.

bessel_j(real nu, real x) -> real

Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:

$$J_{\nu}(x) = \sum_{m=0}^{\infty} \frac{(-1)^m}{m!\,\[Gamma](../../random/Types/gamma/index.md)(m+\nu+1)} \left(\frac{x}{2}\right)^{2m+\nu}$$

Parameters

• nu: The order of the function.
• x: The value at which the function is evaluated.

bessel_j(real nu, bool x) -> real

Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:

$$J_{\nu}(x) = \sum_{m=0}^{\infty} \frac{(-1)^m}{m!\,\[Gamma](../../random/Types/gamma/index.md)(m+\nu+1)} \left(\frac{x}{2}\right)^{2m+\nu}$$

Parameters

• nu: The order of the function.
• x: The value at which the function is evaluated.

bessel_j(bool nu, integer x) -> real

Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:

$$J_{\nu}(x) = \sum_{m=0}^{\infty} \frac{(-1)^m}{m!\,\[Gamma](../../random/Types/gamma/index.md)(m+\nu+1)} \left(\frac{x}{2}\right)^{2m+\nu}$$

Parameters

• nu: The order of the function.
• x: The value at which the function is evaluated.

bessel_j(bool nu, bool x) -> real

Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:

$$J_{\nu}(x) = \sum_{m=0}^{\infty} \frac{(-1)^m}{m!\,\[Gamma](../../random/Types/gamma/index.md)(m+\nu+1)} \left(\frac{x}{2}\right)^{2m+\nu}$$

Parameters

• nu: The order of the function.
• x: The value at which the function is evaluated.

bessel_j(bool nu, real x) -> real

Evaluates the cylindrical Bessel function of the first kind (J) at the given position. Defined as:

$$J_{\nu}(x) = \sum_{m=0}^{\infty} \frac{(-1)^m}{m!\,\[Gamma](../../random/Types/gamma/index.md)(m+\nu+1)} \left(\frac{x}{2}\right)^{2m+\nu}$$

Parameters

• nu: The order of the function.
• x: The value at which the function is evaluated.