Study on <i>r</i>-truncated degenerate Stirling numbers of the second kind

نویسندگان

چکیده

Abstract The degenerate Stirling numbers of the second kind and first kind, which are, respectively, versions appear frequently when we study various some special polynomials. aim this article is to consider r -truncated reduce for = 1, investigate their explicit expressions, properties related identities, in connection with several other

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Stirling Numbers of the Second Kind

The papers [18], [9], [21], [14], [23], [6], [24], [2], [3], [8], [10], [1], [22], [7], [11], [20], [16], [19], [4], [5], [13], [12], [17], and [15] provide the terminology and notation for this paper. For simplicity, we adopt the following convention: k, l, m, n, i, j denote natural numbers, K, N denote non empty subsets of N, K1, N1, M1 denote subsets of N, and X, Y denote sets. Let us consid...

متن کامل

Maximum Stirling Numbers of the Second Kind

Say an integer n is exceptional if the maximum Stirling number of the second kind S(n, k) occurs for two (of necessity consecutive) values of k. We prove that the number of exceptional integers less than or equal to x is O(x), for any ! > 0. We derive a similar result for partitions of n into exactly k integers.

متن کامل

ON (q; r; w)-STIRLING NUMBERS OF THE SECOND KIND

In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly de…ned (q; r; w)Stirling numbers of the second kind. We also obtain q-Bernstein polynomials as a linear combination of (q...

متن کامل

A Summation Rule Using Stirling Numbers of the Second Kind

n m n m Z ^ . W" = 5>(w, jy^Fip, k)(k)j = Zj\S(m, j)(n, j). k=o y=o k=o j=o Notice that the special case for m = 0 is also true. Hence, (2) holds for every m > 0. • Remark Sometimes in applications of the rule function F(n, k) may involve some independent parameters. Moreover, for the particular case in which F(n, k) > 0, so that (j)(n, 0) > 0, the lefthand side of (2) divided by (j)(n, 0) m...

متن کامل

MIXED r-STIRLING NUMBERS OF THE SECOND KIND

The Stirling number of the second kind {k} counts the number of ways to partition a set of n labeled balls into k non-empty unlabeled cells. We extend this problem and give a new statement of the r-Stirling numbers of the second kind and r-Bell numbers. We also introduce the r-mixed Stirling number of the second kind and r-mixed Bell numbers. As an application of our results we obtain a formula...

متن کامل

ذخیره 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: Open Mathematics

سال: 2022

ISSN: ['2391-5455']

DOI: https://doi.org/10.1515/math-2022-0535