Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem
Apstrakt
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.
Ključne reči:
Cosecant integrals / Secant integrals / Cauchy integral theorem / Integral formulas / Riemann zeta function / Hurwitz zeta function / Primary 30E20 / 11M35 / Secondary 11M99 / 33B10Izvor:
Numerical Algorithms, 2008, 49, 1-4, 129-141Finansiranje / projekti:
- Ministry of Science and Environmental Protection, Republic of Serbia under Research Project Number [142025], Natural Sciences and Engineering Research Council of Canada [OGP0007353]
DOI: 10.1007/s11075-008-9158-y
ISSN: 1017-1398
WoS: 000260618800007
Scopus: 2-s2.0-55349123644
Kolekcije
Institucija/grupa
VinčaTY - 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 . .
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