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bessel_i

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NameDescription
bessel_i(bool nu, integer x) -> realEvaluates the modified cylindrical Bessel function of the first kind (I) at the given position. Defined as:...
bessel_i(bool nu, bool x) -> realEvaluates the modified cylindrical Bessel function of the first kind (I) at the given position. Defined as:...
bessel_i(bool nu, real x) -> realEvaluates the modified cylindrical Bessel function of the first kind (I) at the given position. Defined as:...
bessel_i(real nu, bool x) -> realEvaluates the modified cylindrical Bessel function of the first kind (I) at the given position. Defined as:...
bessel_i(real nu, real x) -> realEvaluates the modified cylindrical Bessel function of the first kind (I) at the given position. Defined as:...
bessel_i(real nu, integer x) -> realEvaluates the modified cylindrical Bessel function of the first kind (I) at the given position. Defined as:...
bessel_i(integer nu, bool x) -> realEvaluates the modified cylindrical Bessel function of the first kind (I) at the given position. Defined as:...
bessel_i(integer nu, real x) -> realEvaluates the modified cylindrical Bessel function of the first kind (I) at the given position. Defined as:...
bessel_i(integer nu, integer x) -> realEvaluates the modified cylindrical Bessel function of the first kind (I) at the given position. Defined as:...

bessel_i(bool nu, integer x) -> real​

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

Iν(x)=i−νJν(ix)=∑m=0∞1m! \[Gamma](../../random/Types/gamma/index.md)(m+ν+1)(x2)2m+νI_{\nu}(x) = i^{-\nu} J_{\nu}(ix) = \sum_{m=0}^{\infty} \frac{1}{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_i(bool nu, bool x) -> real​

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

Iν(x)=i−νJν(ix)=∑m=0∞1m! \[Gamma](../../random/Types/gamma/index.md)(m+ν+1)(x2)2m+νI_{\nu}(x) = i^{-\nu} J_{\nu}(ix) = \sum_{m=0}^{\infty} \frac{1}{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_i(bool nu, real x) -> real​

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

Iν(x)=i−νJν(ix)=∑m=0∞1m! \[Gamma](../../random/Types/gamma/index.md)(m+ν+1)(x2)2m+νI_{\nu}(x) = i^{-\nu} J_{\nu}(ix) = \sum_{m=0}^{\infty} \frac{1}{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_i(real nu, bool x) -> real​

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

Iν(x)=i−νJν(ix)=∑m=0∞1m! \[Gamma](../../random/Types/gamma/index.md)(m+ν+1)(x2)2m+νI_{\nu}(x) = i^{-\nu} J_{\nu}(ix) = \sum_{m=0}^{\infty} \frac{1}{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_i(real nu, real x) -> real​

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

Iν(x)=i−νJν(ix)=∑m=0∞1m! \[Gamma](../../random/Types/gamma/index.md)(m+ν+1)(x2)2m+νI_{\nu}(x) = i^{-\nu} J_{\nu}(ix) = \sum_{m=0}^{\infty} \frac{1}{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_i(real nu, integer x) -> real​

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

Iν(x)=i−νJν(ix)=∑m=0∞1m! \[Gamma](../../random/Types/gamma/index.md)(m+ν+1)(x2)2m+νI_{\nu}(x) = i^{-\nu} J_{\nu}(ix) = \sum_{m=0}^{\infty} \frac{1}{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_i(integer nu, bool x) -> real​

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

Iν(x)=i−νJν(ix)=∑m=0∞1m! \[Gamma](../../random/Types/gamma/index.md)(m+ν+1)(x2)2m+νI_{\nu}(x) = i^{-\nu} J_{\nu}(ix) = \sum_{m=0}^{\infty} \frac{1}{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_i(integer nu, real x) -> real​

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

Iν(x)=i−νJν(ix)=∑m=0∞1m! \[Gamma](../../random/Types/gamma/index.md)(m+ν+1)(x2)2m+νI_{\nu}(x) = i^{-\nu} J_{\nu}(ix) = \sum_{m=0}^{\infty} \frac{1}{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_i(integer nu, integer x) -> real​

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

Iν(x)=i−νJν(ix)=∑m=0∞1m! \[Gamma](../../random/Types/gamma/index.md)(m+ν+1)(x2)2m+νI_{\nu}(x) = i^{-\nu} J_{\nu}(ix) = \sum_{m=0}^{\infty} \frac{1}{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.