Sentence examples for kind is given from inspiring English sources

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

The Stirling number of the first kind is given by ( x ) n = x ( x − 1 ) ⋯ ( x − n + 1 ) = ∑ l = 0 n S 1 ( n, l ) x l. (10).

The recurrence relation for the Stirling numbers of the first kind is given by s_{1}(n+1, k)=s_{1}(n,k-1 -ns_{1}(n,k-1 -ns

For (rin 0,1)), Legendre's complete elliptic integral [27] of the second kind is given by mathcal{E}(r)= int_{0}^{pi/2}sqrt{1-r^{2}sin ^{2}(t)},dt.

A relation between the λ-Bernoulli polynomials (mathfrak{B}_{n}(x;lambda)), the Apostol-Daehee polynomials (mathfrak{D}_{n}(x;lambda)) and the Stirling numbers of the second kind is given by the following theorem.

The Stirling number of the first kind is given by the generating function, (x)_{m} =sum_{l=0}^{m} S_{1}(m,l x^{l} quad (mgeq0) (6) and the Stirling number of the second kind is defined by the generating function, bigl(e^{t}-1bigr)^{m} =m!sum _{l=m}^{infty}S_{2}(l,m frac{t^{l}}{l!} quad (mgeq0) (mbox{see [7, 8, 15, 17]}).

and the Stirling numbers of the second kind are given by ( e t − 1 ) n = n !

The electrocapillary curves of the first and second kind are given for platinum in solutions of different composition.

Unsigned Stirling numbers of the first kind are given by x n ̲ = x ( x + 1 ) ⋯ ( x + n − 1 ) = ∑ l = 0 n | S 1 ( n, l ) | x l. (1.5).

We assume that the kth-order normal derivatives of an unknown function are given on lower and upper bases of the rectangle and that homogeneous boundary conditions of the first kind are given on the lateral sides.

Bernard Williams has argued that if the claims of universalism (whether of the consequentialist or Kantian kind) are given pre-eminence, they will alienate people from their "ground projects," where the latter include the deep attachments associated with loyalties.