Values of the derivatives of the cotangent at rational multiples of pi
Апстракт
By elementary arguments, we deduce closed-form expressions for the values of all derivatives of the cotangent function at rational multiples of pi. These formulae are considerably simpler than Similar ones which were found in a different manner by Kolbig. Also, we show that the values of cot((n))(pi x), n epsilon N, at x = 1/2, 1/3, 2/3, 1/4, 3/4, 1/6 and 5/6 are expressible in terms of the values of the Bernoulli polynomials alone. (C) 2008 Elsevier Ltd. All rights reserved.
Кључне речи:
Cotangent function / Simpsons series multisection formula / Bernoulli polynomials / Bernoulli numbers / Hurwitz zeta function / PolylogarithmИзвор:
Applied Mathematics Letters, 2009, 22, 2, 217-220Финансирање / пројекти:
- info:eu-repo/grantAgreement/MESTD/MPN2006-2010/142025/RS//] (RS-MESTD-MPN2006-2010-142025)
DOI: 10.1016/j.aml.2008.03.013
ISSN: 0893-9659
WoS: 000262219200014
Scopus: 2-s2.0-56949101674
Колекције
Институција/група
VinčaTY - JOUR AU - Cvijović, Đurđe PY - 2009 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3246 AB - By elementary arguments, we deduce closed-form expressions for the values of all derivatives of the cotangent function at rational multiples of pi. These formulae are considerably simpler than Similar ones which were found in a different manner by Kolbig. Also, we show that the values of cot((n))(pi x), n epsilon N, at x = 1/2, 1/3, 2/3, 1/4, 3/4, 1/6 and 5/6 are expressible in terms of the values of the Bernoulli polynomials alone. (C) 2008 Elsevier Ltd. All rights reserved. T2 - Applied Mathematics Letters T1 - Values of the derivatives of the cotangent at rational multiples of pi VL - 22 IS - 2 SP - 217 EP - 220 DO - 10.1016/j.aml.2008.03.013 ER -
@article{ author = "Cvijović, Đurđe", year = "2009", abstract = "By elementary arguments, we deduce closed-form expressions for the values of all derivatives of the cotangent function at rational multiples of pi. These formulae are considerably simpler than Similar ones which were found in a different manner by Kolbig. Also, we show that the values of cot((n))(pi x), n epsilon N, at x = 1/2, 1/3, 2/3, 1/4, 3/4, 1/6 and 5/6 are expressible in terms of the values of the Bernoulli polynomials alone. (C) 2008 Elsevier Ltd. All rights reserved.", journal = "Applied Mathematics Letters", title = "Values of the derivatives of the cotangent at rational multiples of pi", volume = "22", number = "2", pages = "217-220", doi = "10.1016/j.aml.2008.03.013" }
Cvijović, Đ.. (2009). Values of the derivatives of the cotangent at rational multiples of pi. in Applied Mathematics Letters, 22(2), 217-220. https://doi.org/10.1016/j.aml.2008.03.013
Cvijović Đ. Values of the derivatives of the cotangent at rational multiples of pi. in Applied Mathematics Letters. 2009;22(2):217-220. doi:10.1016/j.aml.2008.03.013 .
Cvijović, Đurđe, "Values of the derivatives of the cotangent at rational multiples of pi" in Applied Mathematics Letters, 22, no. 2 (2009):217-220, https://doi.org/10.1016/j.aml.2008.03.013 . .