Closed-form formulae for the derivatives of trigonometric functions at rational multiples of pi
Apstrakt
In this sequel to our recent note [D. Cvijovic, Values of the derivatives of the cotangent at rational multiples of pi, Appl. Math. Lett. http://dx.doi.org/10.1016/J.aml.2008.03.013] it is shown, in a unified manner, by making use of some basic properties of certain special functions, such as the Hurwitz zeta function, Lerch zeta function and Legendre chi function, that the values of all derivatives of four trigonometric functions at rational multiples of pi can be expressed in closed form as simple finite sums involving the Bernoulli and Euler polynomials. In addition, some particular cases are considered. (C) 2008 Elsevier Ltd. All rights reserved.
Ključne reči:
Trigonometric functions / Hurwitz zeta function / Legendre chi function / Lerch zeta function / Bernoulli polynomials / Euler polynomialsIzvor:
Applied Mathematics Letters, 2009, 22, 6, 906-909Finansiranje / projekti:
- Ortogonalni sistemi i primene (RS-144004)
Napomena:
- Available under Elsevier user license: https://www.elsevier.com/about/policies/open-access-licenses/elsevier-user-license
DOI: 10.1016/j.aml.2008.07.019
ISSN: 0893-9659
WoS: 000266213800018
Scopus: 2-s2.0-67349186924
Institucija/grupa
VinčaTY - JOUR AU - Cvijović, Đurđe PY - 2009 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3704 AB - In this sequel to our recent note [D. Cvijovic, Values of the derivatives of the cotangent at rational multiples of pi, Appl. Math. Lett. http://dx.doi.org/10.1016/J.aml.2008.03.013] it is shown, in a unified manner, by making use of some basic properties of certain special functions, such as the Hurwitz zeta function, Lerch zeta function and Legendre chi function, that the values of all derivatives of four trigonometric functions at rational multiples of pi can be expressed in closed form as simple finite sums involving the Bernoulli and Euler polynomials. In addition, some particular cases are considered. (C) 2008 Elsevier Ltd. All rights reserved. T2 - Applied Mathematics Letters T1 - Closed-form formulae for the derivatives of trigonometric functions at rational multiples of pi VL - 22 IS - 6 SP - 906 EP - 909 DO - 10.1016/j.aml.2008.07.019 ER -
@article{ author = "Cvijović, Đurđe", year = "2009", abstract = "In this sequel to our recent note [D. Cvijovic, Values of the derivatives of the cotangent at rational multiples of pi, Appl. Math. Lett. http://dx.doi.org/10.1016/J.aml.2008.03.013] it is shown, in a unified manner, by making use of some basic properties of certain special functions, such as the Hurwitz zeta function, Lerch zeta function and Legendre chi function, that the values of all derivatives of four trigonometric functions at rational multiples of pi can be expressed in closed form as simple finite sums involving the Bernoulli and Euler polynomials. In addition, some particular cases are considered. (C) 2008 Elsevier Ltd. All rights reserved.", journal = "Applied Mathematics Letters", title = "Closed-form formulae for the derivatives of trigonometric functions at rational multiples of pi", volume = "22", number = "6", pages = "906-909", doi = "10.1016/j.aml.2008.07.019" }
Cvijović, Đ.. (2009). Closed-form formulae for the derivatives of trigonometric functions at rational multiples of pi. in Applied Mathematics Letters, 22(6), 906-909. https://doi.org/10.1016/j.aml.2008.07.019
Cvijović Đ. Closed-form formulae for the derivatives of trigonometric functions at rational multiples of pi. in Applied Mathematics Letters. 2009;22(6):906-909. doi:10.1016/j.aml.2008.07.019 .
Cvijović, Đurđe, "Closed-form formulae for the derivatives of trigonometric functions at rational multiples of pi" in Applied Mathematics Letters, 22, no. 6 (2009):906-909, https://doi.org/10.1016/j.aml.2008.07.019 . .
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