bessel_k

Overloads

Name	Description
bessel_k(bool nu, integer x) -> real	Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:...
bessel_k(bool nu, real x) -> real	Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:...
bessel_k(real nu, bool x) -> real	Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:...
bessel_k(real nu, real x) -> real	Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:...
bessel_k(real nu, integer x) -> real	Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:...
bessel_k(integer nu, bool x) -> real	Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:...
bessel_k(integer nu, real x) -> real	Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:...
bessel_k(integer nu, integer x) -> real	Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:...
bessel_k(bool nu, bool x) -> real	Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:...

bessel_k(bool nu, integer x) -> real

Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:

$$K_{\nu}(x) = \frac{\pi}{2} \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin(\nu\pi)}$$

Parameters

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

bessel_k(bool nu, real x) -> real

Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:

$$K_{\nu}(x) = \frac{\pi}{2} \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin(\nu\pi)}$$

Parameters

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

bessel_k(real nu, bool x) -> real

Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:

$$K_{\nu}(x) = \frac{\pi}{2} \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin(\nu\pi)}$$

Parameters

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

bessel_k(real nu, real x) -> real

Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:

$$K_{\nu}(x) = \frac{\pi}{2} \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin(\nu\pi)}$$

Parameters

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

bessel_k(real nu, integer x) -> real

Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:

$$K_{\nu}(x) = \frac{\pi}{2} \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin(\nu\pi)}$$

Parameters

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

bessel_k(integer nu, bool x) -> real

Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:

$$K_{\nu}(x) = \frac{\pi}{2} \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin(\nu\pi)}$$

Parameters

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

bessel_k(integer nu, real x) -> real

Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:

$$K_{\nu}(x) = \frac{\pi}{2} \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin(\nu\pi)}$$

Parameters

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

bessel_k(integer nu, integer x) -> real

Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:

$$K_{\nu}(x) = \frac{\pi}{2} \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin(\nu\pi)}$$

Parameters

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

bessel_k(bool nu, bool x) -> real

Evaluates the modified cylindrical Bessel function of the second kind (K) at the given position. Defined as:

$$K_{\nu}(x) = \frac{\pi}{2} \frac{I_{-\nu}(x) - I_{\nu}(x)}{\sin(\nu\pi)}$$

Parameters

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