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  2. Bessel function - Wikipedia

    en.wikipedia.org/wiki/Bessel_function

    The modified Bessel function () = (/) / ⁡ is useful to represent the Laplace distribution as an Exponential-scale mixture of normal distributions. The modified Bessel function of the second kind has also been called by the following names (now rare):

  3. Miller's recurrence algorithm - Wikipedia

    en.wikipedia.org/wiki/Miller's_recurrence_algorithm

    However, the modified Bessel functions of the second kind () also satisfy the same recurrence relation = + + (). The first solution decreases rapidly with . The second solution increases rapidly with . Miller's algorithm provides a numerically stable procedure to obtain the decreasing solution.

  4. Kelvin functions - Wikipedia

    en.wikipedia.org/wiki/Kelvin_functions

    where K ν (z) is the ν th order modified Bessel function of the second kind. These functions are named after William Thomson, 1st Baron Kelvin. While the Kelvin functions are defined as the real and imaginary parts of Bessel functions with x taken to be real, the functions can be analytically continued for complex arguments xe iφ, 0 ≤ φ ...

  5. Bessel polynomials - Wikipedia

    en.wikipedia.org/wiki/Bessel_polynomials

    The Bessel polynomial may also be defined using Bessel functions from which the polynomial draws its ... is a modified Bessel function of the second kind, y n (x) ...

  6. Modified Bessel function of the second kind - Wikipedia

    en.wikipedia.org/?title=Modified_Bessel_function...

    Language links are at the top of the page across from the title.

  7. K-distribution - Wikipedia

    en.wikipedia.org/wiki/K-distribution

    where = is the shape factor, = / is the scale factor, and is the modified Bessel function of second kind. The above two parameter formalization can also be obtained by setting α = 1 {\displaystyle \alpha =1} , v = β {\displaystyle v=\beta } , and b = β / μ {\displaystyle b=\beta /\mu } , albeit with different physical interpretation of b ...

  8. Generalized inverse Gaussian distribution - Wikipedia

    en.wikipedia.org/wiki/Generalized_inverse...

    where K p is a modified Bessel function of the second kind, a > 0, b > 0 and p a real parameter. It is used extensively in geostatistics, statistical linguistics, finance, etc. This distribution was first proposed by Étienne Halphen.

  9. Rayleigh problem - Wikipedia

    en.wikipedia.org/wiki/Rayleigh_problem

    where is the modified Bessel function of the second kind. As t → ∞ {\displaystyle t\rightarrow \infty } , the solution approaches that of a rigid vortex. The force per unit area exerted on the cylinder is