Higher-order tangent and secant numbers
Апстракт
In this paper, the higher-order tangent numbers and higher-order secant numbers, {I(n, k)(n,k=0)(infinity) and {I(n, k)}(n,k=0)(infinity), have been studied in detail. Several known results regarding I(n, k) and I(n, k) have been brought together along with many new results and insights and they all have been proved in a simple and unified manner. In particular, it is shown that the higher-order tangent numbers I(n, k) constitute a special class of the partial multivariate Bell polynomials and that I(n, k) can be computed from the knowledge of I(n, k). In addition, a simple explicit formula involving a double finite sum is deduced for the numbers I(n, k) and it is shown that I(n, k) are linear combinations of the classical tangent numbers T(n). (C) 2011 Elsevier Ltd. All rights reserved.
Кључне речи:
Tangent numbers / Tangent numbers of order k / Secant numbers / Secant numbers of order k / Higher-order (or, generalized) tangent and secant numbers / Derivative polynomialsИзвор:
Computers and Mathematics with Applications, 2011, 62, 4, 1879-1886Финансирање / пројекти:
- Функционални, функционализовани и усавршени нано материјали (RS-45005)
- Динамика нелинеарних физичкохемијских и биохемијских система са моделирањем и предвиђањем њихових понашања под неравнотежним условима (RS-172015)
DOI: 10.1016/j.camwa.2011.06.031
ISSN: 0898-1221
WoS: 000294797400027
Scopus: 2-s2.0-80051802393
Колекције
Институција/група
VinčaTY - JOUR AU - Cvijović, Đurđe PY - 2011 UR - https://vinar.vin.bg.ac.rs/handle/123456789/4478 AB - In this paper, the higher-order tangent numbers and higher-order secant numbers, {I(n, k)(n,k=0)(infinity) and {I(n, k)}(n,k=0)(infinity), have been studied in detail. Several known results regarding I(n, k) and I(n, k) have been brought together along with many new results and insights and they all have been proved in a simple and unified manner. In particular, it is shown that the higher-order tangent numbers I(n, k) constitute a special class of the partial multivariate Bell polynomials and that I(n, k) can be computed from the knowledge of I(n, k). In addition, a simple explicit formula involving a double finite sum is deduced for the numbers I(n, k) and it is shown that I(n, k) are linear combinations of the classical tangent numbers T(n). (C) 2011 Elsevier Ltd. All rights reserved. T2 - Computers and Mathematics with Applications T1 - Higher-order tangent and secant numbers VL - 62 IS - 4 SP - 1879 EP - 1886 DO - 10.1016/j.camwa.2011.06.031 ER -
@article{ author = "Cvijović, Đurđe", year = "2011", abstract = "In this paper, the higher-order tangent numbers and higher-order secant numbers, {I(n, k)(n,k=0)(infinity) and {I(n, k)}(n,k=0)(infinity), have been studied in detail. Several known results regarding I(n, k) and I(n, k) have been brought together along with many new results and insights and they all have been proved in a simple and unified manner. In particular, it is shown that the higher-order tangent numbers I(n, k) constitute a special class of the partial multivariate Bell polynomials and that I(n, k) can be computed from the knowledge of I(n, k). In addition, a simple explicit formula involving a double finite sum is deduced for the numbers I(n, k) and it is shown that I(n, k) are linear combinations of the classical tangent numbers T(n). (C) 2011 Elsevier Ltd. All rights reserved.", journal = "Computers and Mathematics with Applications", title = "Higher-order tangent and secant numbers", volume = "62", number = "4", pages = "1879-1886", doi = "10.1016/j.camwa.2011.06.031" }
Cvijović, Đ.. (2011). Higher-order tangent and secant numbers. in Computers and Mathematics with Applications, 62(4), 1879-1886. https://doi.org/10.1016/j.camwa.2011.06.031
Cvijović Đ. Higher-order tangent and secant numbers. in Computers and Mathematics with Applications. 2011;62(4):1879-1886. doi:10.1016/j.camwa.2011.06.031 .
Cvijović, Đurđe, "Higher-order tangent and secant numbers" in Computers and Mathematics with Applications, 62, no. 4 (2011):1879-1886, https://doi.org/10.1016/j.camwa.2011.06.031 . .
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