Asymptotic Expansions Related to the Wallis Ratio Based on the Bell Polynomials
نویسندگان
چکیده
In this paper, we establish a new asymptotic expansion related to the Wallis ratio. By using exponential Bell polynomials, show that coefficients of can be recursively determined. addition, an explicit expression for is given. Our results improve and generalize existing ones [1].
منابع مشابه
Inequalities and asymptotic expansions associated with the Wallis sequence
We present the asymptotic expansions of functions involving the ratio of gamma functions and provide formulas for determining the coefficients of the asymptotic expansions. As consequences, we obtain the asymptotic expansions of the Wallis sequence. Also, we establish inequalities for the Wallis sequence.
متن کاملAsymptotic analysis of the Bell polynomials by the ray method
We analyze the Bell polynomials Bn(x) asymptotically as n → ∞. We obtain asymptotic approximations from the differential-difference equation which they satisfy, using a discrete version of the ray method. We give some examples showing the accuracy of our formulas.
متن کاملOn degenerate numbers and polynomials related to the Stirling numbers and the Bell polynomials
In this paper, we consider the degenerate numbers Rn(λ) and polynomials Rn(x, λ) related to the Stirling numbers and the Bell polynomials. We also obtain some explicit formulas for degenerate numbers Rn(λ) and polynomials Rn(x, λ). AMS subject classification: 11B68, 11S40, 11S80.
متن کاملthe role of task-based techniques on the acquisition of english language structures by the intermediate efl students
this study examines the effetivenss of task-based activities in helping students learn english language structures for a better communication. initially, a michigan test was administered to the two groups of 52 students majoring in english at the allameh ghotb -e- ravandi university to ensure their homogeneity. the students scores on the grammar part of this test were also regarded as their pre...
15 صفحه اولAsymptotic Bias in Information Estimates and the Exponential (Bell) Polynomials
We present a new derivation of the asymptotic correction for bias in the estimate of information from a finite sample. The new derivation reveals a relationship between information estimates and a sequence of polynomials with combinatorial significance, the exponential (Bell) polynomials, and helps to provide an understanding of the form and behavior of the asymptotic correction for bias.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Asian research journal of mathematics
سال: 2022
ISSN: ['2456-477X']
DOI: https://doi.org/10.9734/arjom/2022/v18i11608