Sentence examples for defined a sequence from inspiring English sources

Starting with arbitrary initial, defined a sequence by (1.20).

For a and, they defined a sequence as follows (1.15).

As discussed in Section 'Data', we defined a sequence as all actions performed by the participant for a program.

For example, in [1], Brand defined a sequence which stems from the Riccati difference equation x n + 1 = a x n + b c x n + d.

They defined a sequence {x n } iteratively by the arbitrary given x0∈C and x n + 1 = β n x n + ( 1 − β n ) Q C [ ( 1 − α n ) ( x n − λA x n ) ], ∀ n ≥ 0, Open image in new window (4).

For a real-valued bounded function f on ([0,1]), Bernstein [2] defined a sequence of polynomials given by begin{aligned} B_{n}(f;x)=sum_{r=0}^{n}f biggl( frac{r}{n} biggr) {binom{n}{r}}x^{r} 1-x ^{n-r}, quad forall xin [0,1]mbox{ and } 1-x ^{n-r}{N} 1-x ^{n-r}ed} to provide a very simple and elegant proof of the Weierstrass approximation theorem.

Define a sequence such that.

To this end, define a sequence by.

Define a sequence such that (3.17).

and define a sequence in by (1.12).

Define a sequence such that, where,  .