with σ = t0 + v0, p = t0v0, and K l the modified Bessel function of the second kind with order l.
where m =..., -1, 0, 1,... and J m is the Bessel function of the first kind with order m.
σ is the scale parameter, and I 0 x) is the modified Bessel function of the first kind with order zero.
In this formula, is the modified Bessel function of the first kind with order zero and and are parameters to be adjusted.
where I 0 is the modified Bessel function of the first kind with order zero, and u is the unit-step function.
(25) We can write this relation in the matrix form as follows: {mathbf{D}}^{ k)} (x) = {mathbf{S}}_{1} { mathbf{B}}^{ k)} (x), (26) where ({mathbf{D}}^{(k) } (x)) is the ((n+1 times k+1)) matrix for the Daehee polynomials of the first kind with order k, and ({mathbf {B}}^{(k) } (x)) is the ((n+1 times k+1)) matrix for the Bernoulli polynomials of order k.
distribution Multivariate scale mixture distribution Constant (Dirac delta) Gaussian, Exponential Laplacian, Gamma K-distribution, Inverse Gaussian Normal Inverse Gaussian, is the scaled squared Mahalanobis distance from the mean, with for the PolSAR case. is a modified Bessel function of the second kind with order.
The random variable |A + N| is Rician distributed, and its probability density function (pdf) is f | A + N | ( x ) = x σ 2 exp − ( x 2 + | A | 2 ) 2 σ 2 I 0 | A | 2 σ 2 x u ( x ), (27) where I 0 is the modified Bessel function of the first kind with order zero, and u is the unit-step function.
where 1F 1 is the confluent hypergeometric function [38]: 1 F 1 − 1 2 ; 1 ; − x = exp − x 2 ( 1 + x ) I 0 x 2 + x I 1 x 2, (30). in which I 1 is the modified Bessel function of the first kind with order one.
We obtain For the derivative of the modified Bessel function of the second kind, we have to compute where I γ is the modified Bessel function of the first kind with order γ (see 38, 39).
