New identities for the partial Bell polynomials
Апстракт
A new explicit closed-form formula for the multivariate (n, k)th partial Bell polynomial B(n,k) (x(1), x(2), .... x(n-k+1)) is deduced. The formula involves multiple summations and makes it possible, for the first time, to easily evaluate Bn,k directly for given values of n and k (n GT = k, k = 2, 3,...). Also, a new addition formula (with respect to k) is found for the polynomials Bn,k and it is shown that they admit a new recurrence relation. Several special cases and consequences are pointed out, and some examples are also given. (C) 2011 Elsevier Ltd. All rights reserved.
Кључне речи:
Partial Bell polynomial / Recurrence relation / Stirling number of the second kindИзвор:
Applied Mathematics Letters, 2011, 24, 9, 1544-1547Финансирање / пројекти:
- Функционални, функционализовани и усавршени нано материјали (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-45005)
- Динамика нелинеарних физичкохемијских и биохемијских система са моделирањем и предвиђањем њихових понашања под неравнотежним условима (RS-MESTD-Basic Research (BR or ON)-172015)
DOI: 10.1016/j.aml.2011.03.043
ISSN: 0893-9659
WoS: 000291512200013
Scopus: 2-s2.0-79956084021
Колекције
Институција/група
VinčaTY - JOUR AU - Cvijović, Đurđe PY - 2011 UR - https://vinar.vin.bg.ac.rs/handle/123456789/4378 AB - A new explicit closed-form formula for the multivariate (n, k)th partial Bell polynomial B(n,k) (x(1), x(2), .... x(n-k+1)) is deduced. The formula involves multiple summations and makes it possible, for the first time, to easily evaluate Bn,k directly for given values of n and k (n GT = k, k = 2, 3,...). Also, a new addition formula (with respect to k) is found for the polynomials Bn,k and it is shown that they admit a new recurrence relation. Several special cases and consequences are pointed out, and some examples are also given. (C) 2011 Elsevier Ltd. All rights reserved. T2 - Applied Mathematics Letters T1 - New identities for the partial Bell polynomials VL - 24 IS - 9 SP - 1544 EP - 1547 DO - 10.1016/j.aml.2011.03.043 ER -
@article{ author = "Cvijović, Đurđe", year = "2011", abstract = "A new explicit closed-form formula for the multivariate (n, k)th partial Bell polynomial B(n,k) (x(1), x(2), .... x(n-k+1)) is deduced. The formula involves multiple summations and makes it possible, for the first time, to easily evaluate Bn,k directly for given values of n and k (n GT = k, k = 2, 3,...). Also, a new addition formula (with respect to k) is found for the polynomials Bn,k and it is shown that they admit a new recurrence relation. Several special cases and consequences are pointed out, and some examples are also given. (C) 2011 Elsevier Ltd. All rights reserved.", journal = "Applied Mathematics Letters", title = "New identities for the partial Bell polynomials", volume = "24", number = "9", pages = "1544-1547", doi = "10.1016/j.aml.2011.03.043" }
Cvijović, Đ.. (2011). New identities for the partial Bell polynomials. in Applied Mathematics Letters, 24(9), 1544-1547. https://doi.org/10.1016/j.aml.2011.03.043
Cvijović Đ. New identities for the partial Bell polynomials. in Applied Mathematics Letters. 2011;24(9):1544-1547. doi:10.1016/j.aml.2011.03.043 .
Cvijović, Đurđe, "New identities for the partial Bell polynomials" in Applied Mathematics Letters, 24, no. 9 (2011):1544-1547, https://doi.org/10.1016/j.aml.2011.03.043 . .