Closed-form summations of Dowkers and related trigonometric sums
Апстракт
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.
Извор:
Journal of Physics. A: Mathematical and Theoretical, 2012, 45, 37Финансирање / пројекти:
- Функционални, функционализовани и усавршени нано материјали (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-45005)
- Динамика нелинеарних физичкохемијских и биохемијских система са моделирањем и предвиђањем њихових понашања под неравнотежним условима (RS-MESTD-Basic Research (BR or ON)-172015)
DOI: 10.1088/1751-8113/45/37/374015
ISSN: 1751-8113; 1751-8121
WoS: 000308801800016
Scopus: 2-s2.0-84866324528
Колекције
Институција/група
VinčaTY - 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 . .