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A function related to a Lagrange-Bürmann series

Paul Bracken (2002)

Czechoslovak Mathematical Journal

An infinite series which arises in certain applications of the Lagrange-Bürmann formula to exponential functions is investigated. Several very exact estimates for the Laplace transform and higher moments of this function are developed.

An accurate approximation of zeta-generalized-Euler-constant functions

Vito Lampret (2010)

Open Mathematics

Zeta-generalized-Euler-constant functions, γ s : = k = 1 1 k s - k k + 1 d x x s and γ ˜ s : = k = 1 - 1 k + 1 1 k s - k k + 1 d x x s defined on the closed interval [0, ∞), where γ(1) is the Euler-Mascheroni constant and γ ˜ (1) = ln 4 π , are studied and estimated with high accuracy.

An asymptotic approximation of Wallis’ sequence

Vito Lampret (2012)

Open Mathematics

An asymptotic approximation of Wallis’ sequence W(n) = Πk=1n 4k 2/(4k 2 − 1) obtained on the base of Stirling’s factorial formula is presented. As a consequence, several accurate new estimates of Wallis’ ratios w(n) = Πk=1n(2k−1)/(2k) are given. Also, an asymptotic approximation of π in terms of Wallis’ sequence W(n) is obtained, together with several double inequalities such as, for example, W ( n ) · ( a n + b n ) < π < W ( n ) · ( a n + b n ' ) with a n = 2 + 1 2 n + 1 + 2 3 ( 2 n + 1 ) 2 - 1 3 n ( 2 n + 1 ) ' b n = 2 33 ( n + 1 ) 2 ' b n ' 1 13 n 2 ' n .

I-convergence theorems for a class of k-positive linear operators

Mehmet Özarslan (2009)

Open Mathematics

In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.

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