In this paper, we consider <i>r</i>-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these num...In this paper, we consider <i>r</i>-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these numbers. Matrix representation and the relation between these numbers and Pascal matrix are given. Furthermore, the distributions of the signless r-central factorial numbers are derived. In addition, connections between these numbers and the Legendre-Stirling numbers are given.展开更多
In this article, we study the generalized Bernoulli learning model based on the probability of success pi = ai /n where i = 1,2,...n 0a1a2ann and n is positive integer. This gives the previous results given by Abdulna...In this article, we study the generalized Bernoulli learning model based on the probability of success pi = ai /n where i = 1,2,...n 0a1a2ann and n is positive integer. This gives the previous results given by Abdulnasser and Khidr [1], Rashad [2] and EL-Desouky and Mahfouz [3] as special cases, where pi = i/n pi = i2/n2 and pi = ip/np respectively. The probability function P(Wn = k) of this model is derived, some properties of the model are obtained and the limiting distribution of the model is given.展开更多
In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating fun...In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers are derived. The relations between these numbers and generalized Stirling numbers of the first and second kind are deduced. Furthermore, some special cases are given. Finally, matrix representation of the relations between Whitney and Stirling numbers is given.展开更多
文摘In this paper, we consider <i>r</i>-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these numbers. Matrix representation and the relation between these numbers and Pascal matrix are given. Furthermore, the distributions of the signless r-central factorial numbers are derived. In addition, connections between these numbers and the Legendre-Stirling numbers are given.
文摘In this article, we study the generalized Bernoulli learning model based on the probability of success pi = ai /n where i = 1,2,...n 0a1a2ann and n is positive integer. This gives the previous results given by Abdulnasser and Khidr [1], Rashad [2] and EL-Desouky and Mahfouz [3] as special cases, where pi = i/n pi = i2/n2 and pi = ip/np respectively. The probability function P(Wn = k) of this model is derived, some properties of the model are obtained and the limiting distribution of the model is given.
文摘In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers are derived. The relations between these numbers and generalized Stirling numbers of the first and second kind are deduced. Furthermore, some special cases are given. Finally, matrix representation of the relations between Whitney and Stirling numbers is given.
