Evaluation of a ln tan integral arising in quantum field theory

Journal of Mathematical Physics

Volumn 49, Issue 9, 2008, Pages

  Coffey, Mark W ^a  

^a Department of Metallurgical and Materials Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54749103927     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2981311     Document Type: Article

References (18)

1. Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions (National Bureau of Standards, Washington, DC, 1972).
2. Bailey, D. H., " A compendium of BBP-type formulas for mathematical constants.," http://crd.lbl.gov/~dhbailey/dhbpapers/bbp-formulas.pdf, 2004.
3. Bailey, D. H., Borwein, J. M., Calkin, N. J., Girgensohn, R., Luke, D. R., and Moll, V. H., Experimental Mathematics in Action (A. K. Peters, Wellesley, MA, 2007).
4. Bailey, D. H. and Borwein, J. M., " Computer-assisted discovery and proof.," in Tapas in Experimental Mathematics, Contemporary Mathematics, edited by, T. Amdeberhan, and, V. Moll, (American Mathematical Society, Providence, 2008), pp. 21-52; http://crd.lbl.gov/~dhbailey/dhbpapers/comp-disc- proof.pdf, 2007.
5. Borwein, J. M. and Broadhurst, D. J., e-print arXiv:hep-th/9811173.
6. Borwein, J. M., Zucker, I. J., and Boersma, J., " The evaluation of character Euler double sums.," Ramanujan J.. 15, 377 (2008).
7. Broadhurst, D. J., " Massive 3-loop Feynman diagrams reducible to SC primitives of algebras of the sixth root of unity.," Eur. Phys. J. C 1434-6044 10.1007/s100520050466 8, 311 (1999).
8. Broadhurst, D. J., e-print arXiv:hep-th/9806174v2.
9. Coffey, M. W. " On a three-dimensional symmetric Ising tetrahedron, and contributions to the theory of the dilogarithm and Clausen functions.," J. Math. Phys. 0022-2488 10.1063/1.2902996 49, 043510 (2008).
10. de Doelder, P. J., " On the Clausen integral Cl2 (θ) and a related integral.," J. Comput. Appl. Math. 0377-0427 10.1016/0377-0427(84) 90007-4 11, 325 (1984).
11. Gradshteyn, I. S. and Ryzhik, I. M., in Table of Integrals, Series, and Products, 7th ed., edited by, A. Jeffrey, and, D. Zwillinger, (Academic, New York, 1980).
12. Grosjean, C. C., " Formulae concerning the computation of the Clausen integral Cl2 (θ).," J. Comput. Appl. Math. 0377-0427 10.1016/0377-0427(84)90008-6 11, 331 (1984).
13. Hansen, E. R., A Table of Series and Products (Prentice-Hall, Englewood Cliffs, NJ, 1975).
14. Lewin, L., Dilogarithms and Associated Functions (Macdonald, London, 1958).
15. Lewin, L., Polylogarithms and Associated Functions (North-Holland, Amsterdam, 1981).
16. Structural Properties of Polylogarithms, edited by, L. Lewin, (American Mathematical Society, Providence, 1991).
17. Lunev, F. A., " Evaluation of two-loop self-energy diagram with three propagators.," Phys. Rev. D 0556-2821 10.1103/PhysRevD.50.7735 50, 7735 (1994); It appears that in Eq. (18), the integrand factor (1-λy) should read (1-λx).
18. Maximon, L. C., " The dilogarithm function for complex argument.," Proc. R. Soc. London, Ser. A 0950-1207 10.1098/rspa.2003.1156 459, 2807 (2003).