TY  - JOUR
AU  - Cvijović, Đurđe
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3778
AB  - Recently, a half-dozen remarkably general families of the finite trigonometric sums were summed in closed-form by choosing a particularly convenient integration contour and making use of the calculus of residues. In this sequel, we show that this procedure can be further extended and we find the summation formulae, in terms of the higher order Bernoulli polynomials and the ordinary Bernoulli polynomials, for four general families of the finite cotangent sums. (C) 2009 Elsevier Inc. All rights reserved.
T2  - Applied Mathematics and Computation
T1  - Summation formulae for finite cotangent sums
VL  - 215
IS  - 3
SP  - 1135
EP  - 1140
DO  - 10.1016/j.amc.2009.06.053
ER  - 

@article{
author = "Cvijović, Đurđe",
year = "2009",
abstract = "Recently, a half-dozen remarkably general families of the finite trigonometric sums were summed in closed-form by choosing a particularly convenient integration contour and making use of the calculus of residues. In this sequel, we show that this procedure can be further extended and we find the summation formulae, in terms of the higher order Bernoulli polynomials and the ordinary Bernoulli polynomials, for four general families of the finite cotangent sums. (C) 2009 Elsevier Inc. All rights reserved.",
journal = "Applied Mathematics and Computation",
title = "Summation formulae for finite cotangent sums",
volume = "215",
number = "3",
pages = "1135-1140",
doi = "10.1016/j.amc.2009.06.053"
}

Cvijović, Đ.. (2009). Summation formulae for finite cotangent sums. in Applied Mathematics and Computation, 215(3), 1135-1140.
https://doi.org/10.1016/j.amc.2009.06.053

Cvijović Đ. Summation formulae for finite cotangent sums. in Applied Mathematics and Computation. 2009;215(3):1135-1140.
doi:10.1016/j.amc.2009.06.053 .

Cvijović, Đurđe, "Summation formulae for finite cotangent sums" in Applied Mathematics and Computation, 215, no. 3 (2009):1135-1140,
https://doi.org/10.1016/j.amc.2009.06.053 . .

TY  - JOUR
AU  - Cvijović, Đurđe
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3642
AB  - Recently, an interesting dilogarithmic integral arising in quantum field theory has been closed-form evaluated in terms of the Clausen function Cl(2)(theta) by Coffey [J. Math. Phys. 49, 093508 (2008)]. It represents the volume of an ideal tetrahedron in hyperbolic space and is involved in two intriguing equivalent conjectures of Borwein and Broadhurst. It is shown here by simple and direct arguments that this integral can be expressed by the triplet of the Clausen function values which are involved in one of the two above-mentioned conjectures.
T2  - Journal of Mathematical Physics
T1  - A dilogarithmic integral arising in quantum field theory
VL  - 50
IS  - 2
DO  - 10.1063/1.3085764
ER  - 

@article{
author = "Cvijović, Đurđe",
year = "2009",
abstract = "Recently, an interesting dilogarithmic integral arising in quantum field theory has been closed-form evaluated in terms of the Clausen function Cl(2)(theta) by Coffey [J. Math. Phys. 49, 093508 (2008)]. It represents the volume of an ideal tetrahedron in hyperbolic space and is involved in two intriguing equivalent conjectures of Borwein and Broadhurst. It is shown here by simple and direct arguments that this integral can be expressed by the triplet of the Clausen function values which are involved in one of the two above-mentioned conjectures.",
journal = "Journal of Mathematical Physics",
title = "A dilogarithmic integral arising in quantum field theory",
volume = "50",
number = "2",
doi = "10.1063/1.3085764"
}

Cvijović, Đ.. (2009). A dilogarithmic integral arising in quantum field theory. in Journal of Mathematical Physics, 50(2).
https://doi.org/10.1063/1.3085764

Cvijović Đ. A dilogarithmic integral arising in quantum field theory. in Journal of Mathematical Physics. 2009;50(2).
doi:10.1063/1.3085764 .

Cvijović, Đurđe, "A dilogarithmic integral arising in quantum field theory" in Journal of Mathematical Physics, 50, no. 2 (2009),
https://doi.org/10.1063/1.3085764 . .

TY  - JOUR
AU  - Cvijović, Đurđe
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3875
AB  - We find simple explicit closed-form formulas for the Fermi-Dirac function F(-n)(z) and Bose-Einstein function B(-n)(z) for arbitrary n is an element of N. The obtained formulas involve the higher tangent numbers defined by Carlitz and Scoville. We present some examples and direct consequences of applying the main results.
T2  - Theoretical and Mathematical Physics
T1  - Fermi-Dirac and Bose-Einstein Functions of Negative Integer Order
VL  - 161
IS  - 3
SP  - 1663
EP  - 1668
DO  - 10.1007/s11232-009-0153-9
ER  - 

@article{
author = "Cvijović, Đurđe",
year = "2009",
abstract = "We find simple explicit closed-form formulas for the Fermi-Dirac function F(-n)(z) and Bose-Einstein function B(-n)(z) for arbitrary n is an element of N. The obtained formulas involve the higher tangent numbers defined by Carlitz and Scoville. We present some examples and direct consequences of applying the main results.",
journal = "Theoretical and Mathematical Physics",
title = "Fermi-Dirac and Bose-Einstein Functions of Negative Integer Order",
volume = "161",
number = "3",
pages = "1663-1668",
doi = "10.1007/s11232-009-0153-9"
}

Cvijović, Đ.. (2009). Fermi-Dirac and Bose-Einstein Functions of Negative Integer Order. in Theoretical and Mathematical Physics, 161(3), 1663-1668.
https://doi.org/10.1007/s11232-009-0153-9

Cvijović Đ. Fermi-Dirac and Bose-Einstein Functions of Negative Integer Order. in Theoretical and Mathematical Physics. 2009;161(3):1663-1668.
doi:10.1007/s11232-009-0153-9 .

Cvijović, Đurđe, "Fermi-Dirac and Bose-Einstein Functions of Negative Integer Order" in Theoretical and Mathematical Physics, 161, no. 3 (2009):1663-1668,
https://doi.org/10.1007/s11232-009-0153-9 . .

TY  - 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 . .

TY  - JOUR
AU  - Cvijović, Đurđe
PY  - 2008
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3546
AB  - Recently, interesting novel summation formulae for hypergeometric-type series containing a digamma function as a factor have been established by Miller (2006 J. Phys. A: Math. Gen. 39 3011 - 20) mainly by exploiting already known results and using certain transformation and reduction formulae in the theory of the Kampe de Feriet double hypergeometric function. It is shown here that these, and several other series of this type, can be closed-form summed by simpler and more direct arguments based only on a derivative formula for the Pochhammer symbol and the theory of the digamma ( or.) function and generalized hypergeometric function. In addition, a new reduction formula for the Kamp e de Feriet function F 1:1;0 (1 2;1) [z, z] is obtained.
T2  - Journal of Physics. A: Mathematical and Theoretical
T1  - Closed-form summations of certain hypergeometric-type series containing the digamma function
VL  - 41
IS  - 45
DO  - 10.1088/1751-8113/41/45/455205
ER  - 

@article{
author = "Cvijović, Đurđe",
year = "2008",
abstract = "Recently, interesting novel summation formulae for hypergeometric-type series containing a digamma function as a factor have been established by Miller (2006 J. Phys. A: Math. Gen. 39 3011 - 20) mainly by exploiting already known results and using certain transformation and reduction formulae in the theory of the Kampe de Feriet double hypergeometric function. It is shown here that these, and several other series of this type, can be closed-form summed by simpler and more direct arguments based only on a derivative formula for the Pochhammer symbol and the theory of the digamma ( or.) function and generalized hypergeometric function. In addition, a new reduction formula for the Kamp e de Feriet function F 1:1;0 (1 2;1) [z, z] is obtained.",
journal = "Journal of Physics. A: Mathematical and Theoretical",
title = "Closed-form summations of certain hypergeometric-type series containing the digamma function",
volume = "41",
number = "45",
doi = "10.1088/1751-8113/41/45/455205"
}

Cvijović, Đ.. (2008). Closed-form summations of certain hypergeometric-type series containing the digamma function. in Journal of Physics. A: Mathematical and Theoretical, 41(45).
https://doi.org/10.1088/1751-8113/41/45/455205

Cvijović Đ. Closed-form summations of certain hypergeometric-type series containing the digamma function. in Journal of Physics. A: Mathematical and Theoretical. 2008;41(45).
doi:10.1088/1751-8113/41/45/455205 .

Cvijović, Đurđe, "Closed-form summations of certain hypergeometric-type series containing the digamma function" in Journal of Physics. A: Mathematical and Theoretical, 41, no. 45 (2008),
https://doi.org/10.1088/1751-8113/41/45/455205 . .