Sentence examples for kind is defined from inspiring English sources

The Stirling number of the first kind is defined by (2.7).

The Stirling number of the second kind is defined by the generating function to be ( e t − 1 ) m = m !

The Stirling number of the second kind is defined by x n = ∑ l = 0 n S 2 ( n, l ) ( x ) l ( n ≧ 0 ).

The Stirling number of the first kind is defined by ( x ) n = x ( x − 1 ) ⋯ ( x − n + 1 ) = ∑ k = 0 n S 1 ( n, k ) x k. (9).

The Stirling number of the first kind is defined by ( x ) n = ∑ l = 0 n S 1 ( n, l ) x l ( n ≥ 0 ) ( see [16] ).

Still by analogy with classical statistic for scalar real random variables defined in ({mathbb {R}^), the second characteristic function (CF) of the second kind is defined as the natural logarithm of the first CF of the second kind.

Let the q-Bessel function of the second kind be defined in terms of (9)–(11).

As is well known, the Stirling numbers S ( l, n ) of the second kind are defined by the generating function to be ( e t − 1 ) n = n !

The Daehee numbers of the first kind are defined by frac{log(1+t)}{t}=sum_{n=0}^{infty}D_{n} frac{t^{n}}{n!} (cf. [7]).

The familiar q-Stirling numbers S ( n, k ) of the second kind are defined by ( e q ( t ) − 1 ) k [ k ] q !

Stirling numbers of the first kind are defined by bigl(log(1+t bigr)^{n} = n! sum _{m=n}^{infty}S_{1} (m,n) {t^{m} over m!}, (7) and the Stirling numbers of the second kind are defined by bigl(e^{t}-1bigr)^{n}= n! sum _{l=n}^{infty}S_{2} (n,l) frac{t^{l}}{l!} quad (n ge0).