ABSTRACT The Universe is currently undergoing accelerated expansion driven by dark energy. Dark energy’s essential nature remains mysterious: one means of revealing it measuring the Universe’s size at different redshifts. This may be done using baryon acoustic oscillation (BAO) feature, a standard ruler in galaxy two-point correlation function (2PCF). In order to measure distance scale, dilates...

Let F(z) be a vector-valued function F C CN, which is analytic at z 0 and meromorphic in a neighborhood of z 0, and let its Maclaurin series be given. In a recent work [J. Approx. Theory, 76 (1994), pp. 89-111] by the author, vector-valued rational approximation procedures for F(z) that are based on its Maclaurin series, were developed, and some of their convergence properties were analyzed in ...

In the paper, by virtue of a derivative formula for ratio two differentiable functions and with help monotonicity rule, authors expand logarithmic expression involving sine function into Maclaurin power series in terms specific determinants prove decreasing property expressions containing function. These results are interesting purely pure mathematics.