Abstract
In this paper, we introduce central complete and incomplete Bell polynomials which can be viewed as generalizations of central Bell polynomials and central factorial numbers of the second kind, and also as ’central’ analogues for complete and incomplete Bell polynomials. Further, some properties and identities for these polynomials are investigated. In particular, we provide explicit formulas for the central complete and incomplete Bell polynomials related to central factorial numbers of the second kind.
Highlights
IntroductionWe introduce central incomplete Bell polynomials Tn,k ( x1 , x2 , · · · , xn−k+1 ) given by
In this paper, we introduce central incomplete Bell polynomials Tn,k ( x1, x2, · · ·, xn−k+1 ) given by ∞ 1 ∞ 1 tm k tn m = T ( x, x · ) −
N =0 i =1 2 and investigate some properties and identities for these polynomials. They can be viewed as generalizations of central Bell polynomials and central factorial numbers of the second kind, and as ‘central’ analogues for complete and incomplete Bell polynomials
Summary
We introduce central incomplete Bell polynomials Tn,k ( x1 , x2 , · · · , xn−k+1 ) given by. N =0 i =1 2 and investigate some properties and identities for these polynomials They can be viewed as generalizations of central Bell polynomials and central factorial numbers of the second kind, and as ‘central’ analogues for complete and incomplete Bell polynomials. We recall that the central factorial numbers T (n, k) of the second kind and the central Bell polynomials Bn ( x ) are given in terms of generating functions by t. We state the new and main results of this paper, where we introduce central incomplete and complete Bell polynomials and investigate some properties and identities for them. We defer more detailed study of the central incomplete and complete Bell polynomials to a later paper
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