Sentence examples for kind are defined from inspiring English sources

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).

The higher-order Cauchy polynomials of the first kind are defined by the generating function to be ( t log ( 1 + t ) ) α ( 1 + t ) − x = ∑ n = 0 ∞ C n ( x ) t n n ! ( α ∈ Z ≥ 0 ), (8).

As is well known, the Bernoulli polynomials of the second kind are defined by the generating function to be t log ( 1 + t ) ( 1 + t ) x = ∑ n = 0 ∞ b n ( x ) t n n ! ( see [1, p.130] ).

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

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

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

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