Solving certain principal value integrals by reduction to the dilogarithm

Physica A: Statistical Mechanics and its Applications

Volumn 234, Issue 1-2, 1996, Pages 581-588

  Lee, M Howard ^a  

^a UNIVERSITY OF GEORGIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; INTEGRATION; MATHEMATICAL TRANSFORMATIONS;

DILOGARITHM FUNCTIONS; HILBERT TRANSFORMS; PRINCIPAL VALUE LOGARITHMIC INTEGRALS;

OPTICS;

EID: 0030395659     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(96)00297-X     Document Type: Article

References (21)

1. See e.g. K.E. Peiponen and E.M. Vartiainen, Phys. Rev. B 44 (1991) 8301. E. M. Vartiainen, K.E. Peiponen and T. Asakura, Opt. Commun. 89 (1992) 37.
2. See e.g. K.E. Peiponen and E.M. Vartiainen, Phys. Rev. B 44 (1991) 8301. E. M. Vartiainen, K.E. Peiponen and T. Asakura, Opt. Commun. 89 (1992) 37.
3. M.H. Lee and O.I. Sindoni, Phys. Rev. A 46 (1992) 3028.
4. K.T.R. Davies, M.L. Glasser and R.W. Davies, Canad. J. Phys. 70 (1992) 656. Also see K.T.R. Davies, M.L. Glasser, V. Protopopescu and F. Tabakin, Math. Models and Methods in Appl. Sci., in press.
5. K.T.R. Davies, M.L. Glasser and R.W. Davies, Canad. J. Phys. 70 (1992) 656. Also see K.T.R. Davies, M.L. Glasser, V. Protopopescu and F. Tabakin, Math. Models and Methods in Appl. Sci., in press.
6. E.T. Whittaker and G.N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1958) p. 117.
7. L. Lewin, Polylogarithms and Associated Functions (North-Holland, New York, 1981).
8. M.H. Lee, Canad. J. Phys. 73 (1995) 108.
9. M.H. Lee, J. Math. Phys. 36 (1995) 1217; Phys. Rev. E 53 (1996) 5488; 54 (1996) 946.
10. M.H. Lee, J. Math. Phys. 36 (1995) 1217; Phys. Rev. E 53 (1996) 5488; 54 (1996) 946.
11. M.H. Lee, J. Math. Phys. 36 (1995) 1217; Phys. Rev. E 53 (1996) 5488; 54 (1996) 946.
12. P.J. Davis and P. Rabinowitz, Methods of Numerical Integrations (Academic Press, New York, 1984).
13. K.T.R. Davies and R.W. Davies, Canad. J. Phys. 67 (1989) 759. K.T.R. Davies, R.W. Davies and G.D. White, J. Math. Phys. 31 (1990) 1356.
14. K.T.R. Davies and R.W. Davies, Canad. J. Phys. 67 (1989) 759. K.T.R. Davies, R.W. Davies and G.D. White, J. Math. Phys. 31 (1990) 1356.
15. D. Zagier, J. Math. Phys. Sci. (Madras) 22 (1988) 13.
16. L. Lewin, ed., Structural Properties of Polylogarithms (Amer. Math. Soc., Providence, RI, 1991).
17. J.M. Ziman, Principles of the theory of solids (Cambridge, University Press, Cambridge, 1979). See p. 278-282. Also see P.L. Nash, R.J. Bell and R. Alexander, J. Modern. Opt. 42 (1995) 1837.
18. J.M. Ziman, Principles of the theory of solids (Cambridge, University Press, Cambridge, 1979). See p. 278-282. Also see P.L. Nash, R.J. Bell and R. Alexander, J. Modern. Opt. 42 (1995) 1837.
19. G.N. Watson, Quart. J. Math. (Oxford) 10 (1939) 266.
20. M.H. Lee and J.T. Nelson, J. Math. Phys. 31 (1990) 689.
21. Table of Integral Transforms II, ed. A. Erdelyi. (McGraw-Hill, New York 1954).