Sentence examples for and the constant factor from inspiring English sources

And the constant factor in (2.1) is the best possible.

where inequality (3.27) is equivalent to (3.26) and the constant factor is the best possible.

where is defined by (2.2) and the constant factor in (3.1) is the best possible.

where α = λ1 + λ2, 0 <α1 <α and the constant factor α λ 1 λ 2 is the best possible.

The corresponding integral form of (1.1) is that (1.2). where, and the constant factor in (1.2) is the best possible value.

It is all known that the inequality (1.1). is called Hilbert theorem for double series [1], where, and the constant factor in (1.1) is the best possible value.

It is evident that (22) is equivalent to (13), and then the constant factor B ( λ 2, λ 2 ) in (22) is still best possible.

Define the Hardy-Hilbert's integral operator as follows: for Then in view of (1.2), it follows that and Since the constant factor in (1.2) is the best possible, we find that (cf.[2]).[2]

And (4.2) is equivalent to (4.1), and the constant factors and are both the best possible.

where inequality (4.8) is equivalent to (4.7) and the constant factors and are both the best possible.

Moreover, Yang [17] gave an inequality with the particular kernel 1 ( 1 + n x ) λ and an interval variable, and proved that the constant factor is the best possible.