Definition 6.2 Let X be a continuous random variable, then it is said to have a beta k-distribution of the first kind with two parameters m and n, if its probability k-density function ( p k d f ) is defined by [8] f k ( x ) = { 1 k β k ( p, q ) x p k − 1 ( 1 − x ) q k − 1, 0 ≤ x ≤ 1 ; p, q, k > 0, 0, elsewhere.
Now, we consider higher-order twisted Daehee polynomials of the second kind with q-parameter.
Now, we consider the twisted Daehee polynomials of the second kind with q-parameter as follows: D ˆ n, ξ, q ( x ) = ξ n ∫ Z p ( − y + x ) n, q d μ 0 ( y ) ( n ≥ 0 ).
In the special case x = 0, D ˆ n, ξ, q ( 0 ) = D ˆ n, ξ, q are called the twisted Daehee numbers of the second kind with q-parameter.
where n is a nonnegative integer and k ∈ N. In the special case, x = 0, D ˆ n, ξ, q ( k ) = D ˆ n, ξ, q ( k ) ( 0 ) are called the higher-order twisted Daehee numbers of the second kind with q-parameter.
Higher-order twisted Daehee polynomials of the second kind with q-parameter are defined by the multivariant p-adic invariant integral on Z p : D ˆ n, ξ, q ( k ) ( x ) = ξ n ∫ Z p ⋯ ∫ Z p ( − x 1 − ⋯ − x k + x ) n, q d μ 0 ( x 1 ) ⋯ d μ 0 ( x k ), (2.22).
The system deals with two kinds of parameters associated with the track: operator defined which is static and deterministic such as the maximum allowable speed on the track, turnout restricted speed.
In this formula, is the modified Bessel function of the first kind with order zero and and are parameters to be adjusted.
And Judd, I'm really beginning to think that the two-hour thing, with parameters and an end in sight, is ideal for this kind of show, and for you.
