TY  - JOUR
AU  - Cvijović, Đurđe
AU  - Srivastava, H. M.
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5038
AB  - Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095-101; 1989 J. Math. Phys. 30 770-3; 1992 J. Phys. A: Math. Gen. 25 2641-8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowkers 75th birthday devoted to Applications of zeta functions and other spectral functions in mathematics and physics.
T2  - Journal of Physics. A: Mathematical and Theoretical
T1  - Closed-form summations of Dowkers and related trigonometric sums
VL  - 45
IS  - 37
DO  - 10.1088/1751-8113/45/37/374015
ER  - 

@article{
author = "Cvijović, Đurđe and Srivastava, H. M.",
year = "2012",
abstract = "Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095-101; 1989 J. Math. Phys. 30 770-3; 1992 J. Phys. A: Math. Gen. 25 2641-8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowkers 75th birthday devoted to Applications of zeta functions and other spectral functions in mathematics and physics.",
journal = "Journal of Physics. A: Mathematical and Theoretical",
title = "Closed-form summations of Dowkers and related trigonometric sums",
volume = "45",
number = "37",
doi = "10.1088/1751-8113/45/37/374015"
}

Cvijović, Đ.,& Srivastava, H. M.. (2012). Closed-form summations of Dowkers and related trigonometric sums. in Journal of Physics. A: Mathematical and Theoretical, 45(37).
https://doi.org/10.1088/1751-8113/45/37/374015

Cvijović Đ, Srivastava HM. Closed-form summations of Dowkers and related trigonometric sums. in Journal of Physics. A: Mathematical and Theoretical. 2012;45(37).
doi:10.1088/1751-8113/45/37/374015 .

Cvijović, Đurđe, Srivastava, H. M., "Closed-form summations of Dowkers and related trigonometric sums" in Journal of Physics. A: Mathematical and Theoretical, 45, no. 37 (2012),
https://doi.org/10.1088/1751-8113/45/37/374015 . .

TY  - JOUR
AU  - Cvijović, Đurđe
AU  - Srivastava, H. M.
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3717
AB  - We examine the Landau constants defined by G(n) := Sigma(n)(m=0) 1/2(4m) ((m) (2m))(2) (n = 0, 1, 2, . . .) by making use of the celebrated Ramanujan formula expressing Gn in terms of the Clausenian (3)F(2) hypergeometric series. It is shown that it could be used to deduce other, mostly new, Ramanujan type formulas for the Landau constants involving the terminating and non-terminating hypergeometric series. In addition, by this approach we derive once again, in a simple and unified manner, almost all of the known results and also establish several new results for G(n). These new results include (for example) the generating function and asymptotic expansions and estimates for G(n).
T2  - Taiwanese Journal of Mathematics / TJM
T1  - Asymptotics of the Landau Constants and Their Relationship with Hypergeometric Functions
VL  - 13
IS  - 3
SP  - 855
EP  - 870
DO  - 10.11650/twjm/1500405444
ER  - 

@article{
author = "Cvijović, Đurđe and Srivastava, H. M.",
year = "2009",
abstract = "We examine the Landau constants defined by G(n) := Sigma(n)(m=0) 1/2(4m) ((m) (2m))(2) (n = 0, 1, 2, . . .) by making use of the celebrated Ramanujan formula expressing Gn in terms of the Clausenian (3)F(2) hypergeometric series. It is shown that it could be used to deduce other, mostly new, Ramanujan type formulas for the Landau constants involving the terminating and non-terminating hypergeometric series. In addition, by this approach we derive once again, in a simple and unified manner, almost all of the known results and also establish several new results for G(n). These new results include (for example) the generating function and asymptotic expansions and estimates for G(n).",
journal = "Taiwanese Journal of Mathematics / TJM",
title = "Asymptotics of the Landau Constants and Their Relationship with Hypergeometric Functions",
volume = "13",
number = "3",
pages = "855-870",
doi = "10.11650/twjm/1500405444"
}

Cvijović, Đ.,& Srivastava, H. M.. (2009). Asymptotics of the Landau Constants and Their Relationship with Hypergeometric Functions. in Taiwanese Journal of Mathematics / TJM, 13(3), 855-870.
https://doi.org/10.11650/twjm/1500405444

Cvijović Đ, Srivastava HM. Asymptotics of the Landau Constants and Their Relationship with Hypergeometric Functions. in Taiwanese Journal of Mathematics / TJM. 2009;13(3):855-870.
doi:10.11650/twjm/1500405444 .

Cvijović, Đurđe, Srivastava, H. M., "Asymptotics of the Landau Constants and Their Relationship with Hypergeometric Functions" in Taiwanese Journal of Mathematics / TJM, 13, no. 3 (2009):855-870,
https://doi.org/10.11650/twjm/1500405444 . .

TY  - JOUR
AU  - Cvijović, Đurđe
AU  - Srivastava, H. M.
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3593
AB  - Four classes of the trigonometric moment integrals are evaluated in closed form in a simple and unified manner by making use of the contour integration in conjunction with the Cauchy integral theorem. In all cases, the closed contour of the same shape is used and it is shown that the integrals are expressible only in terms of the Hurwitz zeta function and elementary functions. A number of interesting (known or new) special cases and consequences of the main results are also considered. (c) 2008 Elsevier Inc. All rights reserved.
T2  - Journal of Mathematical Analysis and Applications
T1  - Evaluations of some classes of the trigonometric moment integrals
VL  - 351
IS  - 1
SP  - 244
EP  - 256
DO  - 10.1016/j.jmaa.2008.10.017
ER  - 

@article{
author = "Cvijović, Đurđe and Srivastava, H. M.",
year = "2009",
abstract = "Four classes of the trigonometric moment integrals are evaluated in closed form in a simple and unified manner by making use of the contour integration in conjunction with the Cauchy integral theorem. In all cases, the closed contour of the same shape is used and it is shown that the integrals are expressible only in terms of the Hurwitz zeta function and elementary functions. A number of interesting (known or new) special cases and consequences of the main results are also considered. (c) 2008 Elsevier Inc. All rights reserved.",
journal = "Journal of Mathematical Analysis and Applications",
title = "Evaluations of some classes of the trigonometric moment integrals",
volume = "351",
number = "1",
pages = "244-256",
doi = "10.1016/j.jmaa.2008.10.017"
}

Cvijović, Đ.,& Srivastava, H. M.. (2009). Evaluations of some classes of the trigonometric moment integrals. in Journal of Mathematical Analysis and Applications, 351(1), 244-256.
https://doi.org/10.1016/j.jmaa.2008.10.017

Cvijović Đ, Srivastava HM. Evaluations of some classes of the trigonometric moment integrals. in Journal of Mathematical Analysis and Applications. 2009;351(1):244-256.
doi:10.1016/j.jmaa.2008.10.017 .

Cvijović, Đurđe, Srivastava, H. M., "Evaluations of some classes of the trigonometric moment integrals" in Journal of Mathematical Analysis and Applications, 351, no. 1 (2009):244-256,
https://doi.org/10.1016/j.jmaa.2008.10.017 . .

TY  - JOUR
AU  - Cvijović, Đurđe
AU  - Srivastava, H. M.
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3721
AB  - It is shown that there exists a companion formula to Srivastavas formula for the Lipschitz-Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000) 77-84] and that together these two results form a discrete Fourier transform pair. This Fourier transform pair makes it possible for other (known or new) results involving the values of various Zeta functions at rational arguments to be easily recovered or deduced in a more general context and in a remarkably unified manner. (C) 2009 Elsevier Ltd. All rights reserved.
T2  - Applied Mathematics Letters
T1  - Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function
VL  - 22
IS  - 7
SP  - 1081
EP  - 1084
DO  - 10.1016/j.aml.2008.08.024
ER  - 

@article{
author = "Cvijović, Đurđe and Srivastava, H. M.",
year = "2009",
abstract = "It is shown that there exists a companion formula to Srivastavas formula for the Lipschitz-Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000) 77-84] and that together these two results form a discrete Fourier transform pair. This Fourier transform pair makes it possible for other (known or new) results involving the values of various Zeta functions at rational arguments to be easily recovered or deduced in a more general context and in a remarkably unified manner. (C) 2009 Elsevier Ltd. All rights reserved.",
journal = "Applied Mathematics Letters",
title = "Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function",
volume = "22",
number = "7",
pages = "1081-1084",
doi = "10.1016/j.aml.2008.08.024"
}

Cvijović, Đ.,& Srivastava, H. M.. (2009). Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function. in Applied Mathematics Letters, 22(7), 1081-1084.
https://doi.org/10.1016/j.aml.2008.08.024

Cvijović Đ, Srivastava HM. Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function. in Applied Mathematics Letters. 2009;22(7):1081-1084.
doi:10.1016/j.aml.2008.08.024 .

Cvijović, Đurđe, Srivastava, H. M., "Some discrete Fourier transform pairs associated with the Lipschitz-Lerch Zeta function" in Applied Mathematics Letters, 22, no. 7 (2009):1081-1084,
https://doi.org/10.1016/j.aml.2008.08.024 . .

TY  - JOUR
AU  - Cvijović, Đurđe
AU  - Srivastava, H. M.
PY  - 2008
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3559
AB  - It is shown in this paper, by making use of contour integration and the Cauchy integral theorem, that two general families of definite integrals can be evaluated in closed form and are expressible only in terms of the Hurwitz zeta function and elementary functions. In addition, a number of interesting (known or new) special cases and consequences of the main results are considered and some comparison with results of symbolic computation is made.
T2  - Numerical Algorithms
T1  - Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem
VL  - 49
IS  - 1-4
SP  - 129
EP  - 141
DO  - 10.1007/s11075-008-9158-y
ER  - 

@article{
author = "Cvijović, Đurđe and Srivastava, H. M.",
year = "2008",
abstract = "It is shown in this paper, by making use of contour integration and the Cauchy integral theorem, that two general families of definite integrals can be evaluated in closed form and are expressible only in terms of the Hurwitz zeta function and elementary functions. In addition, a number of interesting (known or new) special cases and consequences of the main results are considered and some comparison with results of symbolic computation is made.",
journal = "Numerical Algorithms",
title = "Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem",
volume = "49",
number = "1-4",
pages = "129-141",
doi = "10.1007/s11075-008-9158-y"
}

Cvijović, Đ.,& Srivastava, H. M.. (2008). Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem. in Numerical Algorithms, 49(1-4), 129-141.
https://doi.org/10.1007/s11075-008-9158-y

Cvijović Đ, Srivastava HM. Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem. in Numerical Algorithms. 2008;49(1-4):129-141.
doi:10.1007/s11075-008-9158-y .

Cvijović, Đurđe, Srivastava, H. M., "Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem" in Numerical Algorithms, 49, no. 1-4 (2008):129-141,
https://doi.org/10.1007/s11075-008-9158-y . .

TY  - JOUR
AU  - Cvijović, Đurđe
AU  - Srivastava, H. M.
PY  - 2007
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3187
AB  - Finite sums of powers of cosecants appear in a wide range of physical problems. We, through a unified approach which uses contour integrals and residues, establish the summation formulas for two general families of such sums. One of them is the family which was first studied and summed in closed form by Dowker [Phys. Rev. D 36, 3095 (1987)], while the other is related to it and has not been studied before. Our summation formulas of the Dowker sums involve only the Stirling numbers of the first kind and the (ordinary) Bernoulli polynomials and numbers, unlike the earlier summation formulas in which either the higher-order Bernoulli numbers and polynomials or the multiple sums involving the Bernoulli numbers and their products, were used. A great deal of other (known or presumably new) closed-form summations follows as straightforward corollaries to these formulas. Among them are two special cases of the celebrated Verlindes formula and numerous sums encountered in various physical problems by McCoy and Orrick [J. Stat. Phys. 83, 839 (1996)], Gervois and Mehta [J. Math. Phys. 36, 5098 (1995)], and Henkel and Lacki [Phys. Lett. A 138, 105 (1989)]. (c) 2007 American Institute of Physics.
T2  - Journal of Mathematical Physics
T1  - Closed-form summation of the Dowker and related sums
VL  - 48
IS  - 4
DO  - 10.1063/1.2712895
ER  - 

@article{
author = "Cvijović, Đurđe and Srivastava, H. M.",
year = "2007",
abstract = "Finite sums of powers of cosecants appear in a wide range of physical problems. We, through a unified approach which uses contour integrals and residues, establish the summation formulas for two general families of such sums. One of them is the family which was first studied and summed in closed form by Dowker [Phys. Rev. D 36, 3095 (1987)], while the other is related to it and has not been studied before. Our summation formulas of the Dowker sums involve only the Stirling numbers of the first kind and the (ordinary) Bernoulli polynomials and numbers, unlike the earlier summation formulas in which either the higher-order Bernoulli numbers and polynomials or the multiple sums involving the Bernoulli numbers and their products, were used. A great deal of other (known or presumably new) closed-form summations follows as straightforward corollaries to these formulas. Among them are two special cases of the celebrated Verlindes formula and numerous sums encountered in various physical problems by McCoy and Orrick [J. Stat. Phys. 83, 839 (1996)], Gervois and Mehta [J. Math. Phys. 36, 5098 (1995)], and Henkel and Lacki [Phys. Lett. A 138, 105 (1989)]. (c) 2007 American Institute of Physics.",
journal = "Journal of Mathematical Physics",
title = "Closed-form summation of the Dowker and related sums",
volume = "48",
number = "4",
doi = "10.1063/1.2712895"
}

Cvijović, Đ.,& Srivastava, H. M.. (2007). Closed-form summation of the Dowker and related sums. in Journal of Mathematical Physics, 48(4).
https://doi.org/10.1063/1.2712895

Cvijović Đ, Srivastava HM. Closed-form summation of the Dowker and related sums. in Journal of Mathematical Physics. 2007;48(4).
doi:10.1063/1.2712895 .

Cvijović, Đurđe, Srivastava, H. M., "Closed-form summation of the Dowker and related sums" in Journal of Mathematical Physics, 48, no. 4 (2007),
https://doi.org/10.1063/1.2712895 . .

TY  - JOUR
AU  - Cvijović, Đurđe
AU  - Srivastava, H. M.
PY  - 2007
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3207
AB  - We use contour integrals and the Cauchy residue theorem in order to derive several summation formulas, in terms of the higher-order Bernoulli polynomials and the ordinary Bernoulli and Euler polynomials, for a remarkably general family of secant sums. Numerous (known or new) special cases are shown to follow readily from the summation formulas presented in this paper. (c) 2007 Elsevier Inc. All rights reserved.
T2  - Applied Mathematics and Computation
T1  - Summation of a family of finite secant sums
VL  - 190
IS  - 1
SP  - 590
EP  - 598
DO  - 10.1016/j.amc.2007.01.054
ER  - 

@article{
author = "Cvijović, Đurđe and Srivastava, H. M.",
year = "2007",
abstract = "We use contour integrals and the Cauchy residue theorem in order to derive several summation formulas, in terms of the higher-order Bernoulli polynomials and the ordinary Bernoulli and Euler polynomials, for a remarkably general family of secant sums. Numerous (known or new) special cases are shown to follow readily from the summation formulas presented in this paper. (c) 2007 Elsevier Inc. All rights reserved.",
journal = "Applied Mathematics and Computation",
title = "Summation of a family of finite secant sums",
volume = "190",
number = "1",
pages = "590-598",
doi = "10.1016/j.amc.2007.01.054"
}

Cvijović, Đ.,& Srivastava, H. M.. (2007). Summation of a family of finite secant sums. in Applied Mathematics and Computation, 190(1), 590-598.
https://doi.org/10.1016/j.amc.2007.01.054

Cvijović Đ, Srivastava HM. Summation of a family of finite secant sums. in Applied Mathematics and Computation. 2007;190(1):590-598.
doi:10.1016/j.amc.2007.01.054 .

Cvijović, Đurđe, Srivastava, H. M., "Summation of a family of finite secant sums" in Applied Mathematics and Computation, 190, no. 1 (2007):590-598,
https://doi.org/10.1016/j.amc.2007.01.054 . .