Derivative polynomials and closed-form higher derivative formulae
Апстракт
In a recent paper, Adamchik [1] expressed in a closed-form symbolic derivatives of four functions belonging to the class of functions whose derivatives are polynomials in terms of the same functions. In this sequel, simple closed-form higher derivative formulae which involve the Carlitz-Scoville higher order tangent and secant numbers are derived for eight trigonometric and hyperbolic functions. (C) 2009 Elsevier Inc. All rights reserved.
Кључне речи:
Closed-form formula / Tangent numbers of order k / Secant numbers of order k / Higher (generalized) tangent numbers / Higher (generalized) secant numbers / Derivative formula / Derivative polynomialsИзвор:
Applied Mathematics and Computation, 2009, 215, 8, 2002-3006Финансирање / пројекти:
- Ministry of Science of the Republic of Serbia [142025, 144004]
DOI: 10.1016/j.amc.2009.09.047
ISSN: 0096-3003
WoS: 000271936400023
Scopus: 2-s2.0-71849118257
Колекције
Институција/група
VinčaTY - JOUR AU - Cvijović, Đurđe PY - 2009 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3827 AB - In a recent paper, Adamchik [1] expressed in a closed-form symbolic derivatives of four functions belonging to the class of functions whose derivatives are polynomials in terms of the same functions. In this sequel, simple closed-form higher derivative formulae which involve the Carlitz-Scoville higher order tangent and secant numbers are derived for eight trigonometric and hyperbolic functions. (C) 2009 Elsevier Inc. All rights reserved. T2 - Applied Mathematics and Computation T1 - Derivative polynomials and closed-form higher derivative formulae VL - 215 IS - 8 SP - 2002 EP - 3006 DO - 10.1016/j.amc.2009.09.047 ER -
@article{ author = "Cvijović, Đurđe", year = "2009", abstract = "In a recent paper, Adamchik [1] expressed in a closed-form symbolic derivatives of four functions belonging to the class of functions whose derivatives are polynomials in terms of the same functions. In this sequel, simple closed-form higher derivative formulae which involve the Carlitz-Scoville higher order tangent and secant numbers are derived for eight trigonometric and hyperbolic functions. (C) 2009 Elsevier Inc. All rights reserved.", journal = "Applied Mathematics and Computation", title = "Derivative polynomials and closed-form higher derivative formulae", volume = "215", number = "8", pages = "2002-3006", doi = "10.1016/j.amc.2009.09.047" }
Cvijović, Đ.. (2009). Derivative polynomials and closed-form higher derivative formulae. in Applied Mathematics and Computation, 215(8), 2002-3006. https://doi.org/10.1016/j.amc.2009.09.047
Cvijović Đ. Derivative polynomials and closed-form higher derivative formulae. in Applied Mathematics and Computation. 2009;215(8):2002-3006. doi:10.1016/j.amc.2009.09.047 .
Cvijović, Đurđe, "Derivative polynomials and closed-form higher derivative formulae" in Applied Mathematics and Computation, 215, no. 8 (2009):2002-3006, https://doi.org/10.1016/j.amc.2009.09.047 . .